A number squared is defined as the number multiplied by itself. In this problem, given a number n, print the number $$$n^{2}$$$.

Basic math operations are very important in programming applications. In this problem, your task is to calculate the product of two integers, multiplied by three.

Triangles are one of the simplest geometric shapes. Equilateral triangles have the special property of all three of their sides being equal to each other. In this problem, you will be given a list of side lengths of equilateral triangles. You should find the sum of the perimeters of the triangles, given that the triangles are all equilateral.

The sum of the angles in a triangle is 180, and the sum of the angles in a square is 360. In fact, the sum of angles in any polygon increases by 180 with each side added to the polygon. In this problem, you must figure out the sum of angles of a polygon, given its number of sides.

Take in a number from 1 through 1000, print Fizz if the number is divisible by 3, print Buzz if the number is divisible by 5, or FizzBuzz if the number is divisible by both. If none of these conditions are true, print nothing

Find the distance between two 2D points. Remember that the distance formula is

$$$d = \sqrt{(x_{2} - x_{1})^2 + (y_{2}-y_{1})^2}$$$

math.sqrt will calculate the square root of a number. Also, you also have to add the line import math at the top of the program.

You have a clock that tells time in the usual way: hours, minutes, and seconds. When you wake up in the morning, you want to figure out how many seconds you slept for. Conveniently, you fell asleep the night before at exactly 12:00 AM. Remember that there are 60 seconds in a minute and 60 minutes in an hour.

Calculate the distance between two points of a specified dimension. The common distance formula still applies to higher dimensional points with a small modification. You will input two points and display the distance between them as you normally would with the distance formula.

The n-dimensional distance formula can be expressed as

$$$d(p,q) = \sqrt{(q_{1}-p_{1})^2 + (q_{2}-p_{2})^2 + ... + (q_{n}-p_{n})^2}$$$

or in other terms:

$$$\sqrt{\sum_{i=1}^{n} (q_{i}-p_{i})^2} = d$$$

Remember that math.sqrt will calculate the square root of a number (you also have to add the line import math at the top of the program).

A hello world program is an essential starting point for all coders. In this problem, write a program to print out "Hello CodeRams".

In Python, you can print text using the print command. So, for this problem, type print("Hello CodeRams").

You can download Python here.

Your favorite basketball player is the leading scorer in the country, and you want to know exactly how good they are. Points per game is measured as points divided by games played, and is used to rank leading scorers in basketball.

Your favorite ski resort has a certain number of easy trails, more difficult trails, most difficult trails, and expert-only trails. Given these values, find how many trails there are at the ski resort. Note that the same trail will never be two different difficulties.

In the last contest, you were asked to find the last digit of a very large number. This time, you are asked to find the entirety of a much smaller number: your task is to find the first number taken to the power of second number. A brute force approach does work here.

When two resistors with resistances a and b are parallel in an electronic circuit, their equivalent resistance is calculated as (a * b) / (a + b). Given the resistances of two resistors, calculate their equivalent resistance.

You find yourself stuck in a labyrinth and don't know your way out! There are several dangerous traps placed throughout the labyrinth. You need to find a way out, but first you need to know how many traps there are in the labyrinth.

You're going to a large city with a complex subway system. You need to find out how many subway lines you will take from the airport to your hotel. Given a list of stations that each subway line stops at, print the minimum number of lines you need to take to get from the airport to your hotel.

While testing your gravity vehicle for Science Olympiad, you have decided to test the vehicle both on Earth, and on Mars. You want to know the gravitational constant of the planet that you are currently testing the vehicle on. You are given that the gravitational constant on Earth is 9.807 m/s^2 and the gravitational constant on Mars is 3.711 m/s^2.

While preparing for Chemistry Lab in Science Olympiad, you are taught to "cross your charges" when calculating the molecular coefficients given the charges: using the charges of two bonded ions, you swap the two values to obtain the molecular coefficients. For example, a molecule made of two ions with charges of 4 and 3 would have coefficients of 3 and 4, respectively.

In mechanical engineering, the primary tool used to measure the energy amplified into a simple machine or a compound machine is called a concept known as the Mechanical Advantage, which signifies the ratio of the energy put into a machine, and the amount of force it outputs.

In one type of simple machine, the lever, mechanical advantage will be calculated by the lengths of the two sides, with the position of the fulcrum determining the length of the two sides. A diagram and a simplified formula of this process has been given below:

You are working on your Boomilevers for Science Olympiad, an event that requires the breaking of various "boomilevers". For this problem, you are given a list of numbers representing the force you applied to each boomilever in pounds. You know a certain number of pounds that will always break any boomilever. Given these values, calculate how many of your boomilevers have broken so far.

Encryption has been an essential tool throughout history and the modern world. Essentially, encryption is the practice of encoding messages, for the purposes of securing the message's confidentiality from other parties.

While testing your hovercraft for Science Olympiad, the hovercraft flew over a pile of boxes in your basement and traveled a total distance of n feet. Given that the boxes are in a rectangular shape, and that the hovercraft took off and landed at opposite corners of the pile of boxes, calculate how far you will have to walk to pick up the hovercraft. You are also given the length of one side of the pile of boxes.

Uh oh! You are working on building an analog thermometer using nonlinear components, so how can you calibrate your temperature sensor with test data? You can use a form of nonlinear regression in the form of the Steinhart-Hart equation, an equation designed to explain the relation between the electrical resistance of a solid and its temperature. While this task may sound difficult, it is actually quite simple using the equation. The Steinhart-Hart equation itself has three calculated constants(A,B, and C), and takes in a value R, which is the resistance of the metal.

The equation is represented as:

$$$\frac1T = A + B(lnR) + C(lnR)^3$$$

This equation is useful for the process of actual temperature determination, but we still need to calculate the constants A, B, and C before we can use it. To find these values, we must first find three resistance to temperature data points, which are usually discovered through experimentation. For this problem, these data points will be provided and you will be required to find the A, B, and C constants. The process of finding these values involves calculating a series of equations. These equations are as follows:

$$$L_1 = lnR_1$$$

$$$L_2 = lnR_2$$$

$$$L_3 = lnR_3$$$

$$$Y_1 = \frac{1}{T_1}$$$

$$$Y_2 = \frac{1}{T_2}$$$

$$$Y_3 = \frac{1}{T_3}$$$

$$$\gamma_2 = (Y_2-Y_1)/(L_2-L_1)$$$

$$$\gamma_3 = (Y_3-Y_1)/(L_3-L_1)$$$

$$$C = ((\gamma_3-\gamma_2)/(L_3-L_2))*(L1+L2+L3)^{-1}$$$

$$$B = \gamma_2-C(L_1^2+L_1L_2+L_2^2)$$$

$$$A = Y_1 - L_1(B+L_1^2C)$$$

For this problem, you will be given R1, R2, R3, T1, T2, and T3. You are tasked with then calculating the value for A, you will not have to return B and C considering that a valid number for A will imply correct values for B and C.

You are currently working on Ping Pong Parachute for Science Olympiad and you want to test how high your rocket is going. The only problem is that your dog ate your altimeter, so now you can no longer use it to measure the rocket's height. Luckily you happen to have a PhD in physics and you can just calculate how high the rocket will go. Not only do you have a PhD, but you also have a speedometer, so you can see the speed of the rocket when it takes off(Initial velocity). The equation $$$V_f^2 = V_i^2 + 2ad$$$ to represent the height of the rocket.

$$$V_i$$$ = initial velocity

$$$V_f$$$ = speed of the rocket at its highest point (Hint: Its not moving)

a = acceleration due to gravity (-9.8 $$$m/s^2$$$)

d = height of the rocket

While you were at science olympiad, you missed your favorite basketball team's biggest game of the year. You don't know the score, but you know the number of baskets, three-pointers, and free throws made by each team. Your task is to figure out which team won the game based on the given information. Recall that a three-pointer is worth 3 points, a regular basket is worth 2 points, and a free throw is worth one point. The number of baskets made includes three-pointers and two-pointers, but not free throws.

You are the "do-er" for the Science Olympiad event "Write it, Do it", which means that you have to interpret your event partner's written description of an object and replicate the object based on the description. Unfortunately, your partner is bad at spelling and misspelled a critical word in the description. Your task is to figure out which word your partner most likely meant to write.

Making the rules for a competition is an important part of an online competition. For this problem, you will read the rules in the input, and print them out to the screen.

To take in input, you can use the input() command. To print out exactly what is inputted, you would do print(input()).

For this problem, you'll need to print "Competition Rules:", AND the input, on two separate lines. You should use two separate print statements.

You have made $$$n$$$ payments in the past year, and you would like to figure out how much money you have spent in total, in cents.

You consider a number to be funny if it is divisible by both 5 and 7. Given a number, figure out whether or not it is a funny number.

Your favorite soccer announcer will always say "gooooal" for a very long time after a team scores. You have a "speech to text" tool that transcribed the announcer's words. Given his written down goal reaction, figure out exactly how many "o" letters are in it.

While watching the world cup, you wonder how many points your team has in the group stage. Recall that during the group stage teams are awarded three points for a win, one point for a tie, and zero points for a loss. For this problem, figure out how many group stage points your team has based on their record (wins, losses, and ties).

While listening to an orchestra fail to play the music from 2001: A Space Odyssey, you wonder what the lowest positive number (other than one) that divides 2001 is. It turns out to be 3 (2001 = 3 * 667). Write a program to find this value for any composite number $$$n$$$.

Unfortunately, you have been sent to prison because you solved too many problems at CodeQuest 2021. Now, you're trying to break out. Your cell has a combination lock with $$$n$$$ dials. You're planning to try all of the possible combinations of the lock, and you want to know how many possible combinations the lock has.

While watching a basketball game, you wonder what your team's total free throw percentage is. You are given how many free throws each player on your team has made and attempted. Given these values, calculate your team's free throw percentage.

You have a broken ladder. Your ladder would normally have $$$n$$$ rungs numbered from 1 to $$$n$$$, but unfortunately some of the rungs have broken off. You can only climb up the ladder if the minimum gap between rungs is less than or equal to some value $$$k$$$. For example, if $$$k$$$ = 1, if the ladder was broken at all, you would not be able to climb the ladder.

You have a list of numbers. You want to figure out how many distinct (different) numbers are in the list. For example, the list [1, 2, 3, 4, 4, 5, 5] has 5 distinct numbers.

You are going on a long road trip, and want to know what the maximum speed limit is in each state that you are traveling through.

You've just bought a set of practice katanas, which have an item number of 1101-1816. While staring at this item number, you wonder what the LCM (Least Common Multiple) of 1101 and 1816 is.

To calculate the LCM of two numbers, you can multiply the two numbers together, and divide this result by the GCD (Greatest Common Divisor) of the two numbers. For example, let's take the numbers 60 and 72. Their GCD is 12 (12 is the greatest number that divides both numbers), their product (60 x 72) is 4320, and their GCD is 4320 / 12 = 360. To calculate the GCD of two numbers, you can use this recursive formula:

gcd(a, b) = a, if b = 0

otherwise, gcd(a, b) = gcd(b, a mod b)

You are given a shuffled deck of cards, and your task is to return them to sorted order. Sorted order involves the cards being sorted first by their numbers, and if their numbers are equal, being sorted by their suit. In the sorting, clubs comes before diamonds, which comes before hearts, which comes before spades. The deck may not be complete, i.e. some cards may be missing. Assume that aces are always the highest possible card for this problem.

You are using a code where letters in words map to digits in the following way:

0 = o

1 = i

3 = e

4 = a

5 = s

7 = t

(the other digits will not be used in this problem)

You've found a sequence of numbers, and you want to find which words the numbers correspond to using the code described above. For this problem, assume that the only letters in each word are the ones that map to numbers.

Sudoku is a popular number puzzle involving placing digits (1-9) in a 9 by 9 grid. A sudoku is considered valid if all of the following are true:

-All digits are integers from 1 to 9

-No number occurs in the same row twice

-No number occurs in the same column twice

-No number occurs in the same 3 by 3 box twice.

Given a sudoku board, print whether or not it is valid.

While watching the world cup, you wonder how many points each team has in the group stage. Recall that during the group stage teams are awarded three points for a win, one point for a tie, and zero points for a loss. For this problem, you're given a history of the games between all of the teams, and you must figure out how many group stage points each team has.

Note: this is a harder version of a previous problem in the contest.

You are using a code where letters in words map to digits in the following way:

0 = o

1 = i

3 = e

4 = a

5 = s

7 = t

(the other digits will not be used in this problem)

You've found a sequence of numbers, and you want to find how many words the numbers correspond to using the code described above.

Additionally, for this problem, assume that any letters in the original word that did not map to a letter in the code were simply encoded as blanks. Thus, a number sequence can potentially map to multiple words. Thus, you are given a dictionary of words, and you are tasked with figuring out which words in the dictionary map to the given number sequence.

Your team qualified for the national finals of CodeQuest 2021*, and you need to figure out which flights you need to take to get to the location of the finals. However, you have a limited budget for the whole trip. Figure out the best route for your team to go to the specified location of the competition, given the possible flights and their times. If multiple routes are possible, choose the one that has the lowest price. Assume there are no layovers in airports, i.e. all of the time spent on a journey is spent on the airplanes. Your starting location is always "Syracuse"

Yoda tends to confuse people with his irregular syntax. Write a program that takes in a string and switches the first half of the words with the second half.

You are on planet Omicron Persei VIII and you find that the force due to gravity on you is Fg newtons, you also know that you have a mass of M. Using this information you want to know how long it will take for an object to fall (time T in seconds) a distance D starting from rest (Vi speed when the object is initially released). Using the following equations Fg = MG and D = ViT+½GT^2.

Given two strings that represent binary numbers, return the sum of the 2 numbers in binary.

Two runners are racing against each other in the 400 meter dash and you want to know who will win. The current distance covered by each runner(meters) and the speed (meters per second) will be given for each runner. Return whether the first or the second runner will end up winning the race assuming they travel at the speed throughout the remainder of the race.

Your 5 year old cousin needs your help with some basic math. Write a program for him to do addition and subtraction.

A monoalphabetic cipher is a type of encryption where each letter in the alphabet correlates to another letter in the alphabet. For this question you need to decrypt a piece of text given the key used to encrypt it and the encrypted message.

Given two arrays of integers, check if they are equal... But, if the arrays can be made equal through the removal of duplicates or sorting, they are equal.

You will be given two opposite corners of two separate rectangles and you must determine whether they intersect or not.

You and your friend are passing notes in class, but to secure the safety of your notes you both decide to scramble the words. Your friend is going to pass you the first note, so that you can figure out the type of scramble that was used. Use the example test case below to figure out how the words where scrambled and write a program that will scramble words in the same way.

Given a tic-tac-toe board, return if you can win the game in one move or not.

You have a meeting on a specific date. Given the current date and the date of the meeting, return how many days there are until the meeting.

A train station needs your help to maximize its efficiency. The train station can only have 100 train carts parked on a track at once, and it is imperative that the tracks are fully filled as to maximize profit. Given a list of trains and their lengths (number of train carts) print the pairs of trains that will most effectively fill the station.

You like to use your stopwatch all the time, but there is one major problem with it. The stopwatch only displays seconds, so when it says 472 seconds have passed you have no idea what that means. Given a time in seconds display the years, days, hours, minutes and seconds that have passed.

You are currently playing minecraft with your friends when you get a brilliant idea for a prank, you want to fill his entire house with sand. Given some information that represents the dimensions of your friend's house return the number of blocks of sand needed to fill it up.

Take a single string S as input, then make all capital characters lowercase and all lowercase characters capital.

Take a single String as input, and output the same string after repeating certain characters by a certain number. The character 'h' should be repeated 5 times, the character 'c' should be repeated 2 times, and the character 'z' should be repeated 12 times.

Find the largest possible number that can be stored with N bits. Assume that the number is a signed integer value. Remember that the maximum value possible with a certain number of bits can be calculated with the formula $$$2^{N-1}-1$$$. When solving this problem, keep in mind that if the input is greater than 32, your programming language may not have large enough integers, so you will need to use larger variable types or arbitrary precision arithmetic. Arbitrary-precision arithmetic comes with most programming languages, for example the BigInteger class in Java.

A compass has many divisions of cardinal directions, most commonly the four cardinal directions of North, East, South, and West are used, though smaller subdivisions called half winds are available. The half winds can be seen on a 16-wind compass rose, and are north-northeast(NNE), east-northeast(ENE), east-southeast(ESE), south-southeast(SSE), south-southwest(SSW), west-southwest(WSW), west-northwest(WNW) and north-northwest(NNW). For this problem, decode the acronym into the full name of the half wind direction.

Given a string S and a list of characters C, print string S after removing all of the characters given in list C.

The event horizon of a black hole, also known as the Schwarzschild radius, is the radius from a black hole at which even light can no longer escape. The formula to calculate the Schwarzschild radius of a given mass is $$$r_s=\frac{2GM}{c^2}$$$. The value $$$G$$$ is the universal gravitational constant, which you should consider to be $$$6.67*10^{-1}$$$ for this problem. $$$G$$$ is being given such a high value under the assumption that the masses being input will be incredibly large. The value of $$$M$$$ will be provided, and the value of $$$c$$$ is the speed of light, which you should consider to be $$$3*10^{4}$$$ for this problem. The value of $$$c$$$ is being decreased due to the incredibly low values that it normally produces.

When using an automobile, one often seeks to understand what they will be expected to pay for the usage of gas resources. The cost of driving a certain distance can be calculated based on the miles per gallon(mpg) of the car, the distance traveled, and the cost per gallon currently. Taking in these three values as input, determine the total cost of the trip.

When performing calculations on linear equations, finding the intersection point of two lines is a very common task. Write a program that takes two linear equations in the form of $$$y=mx+b$$$ and outputs the $$$x$$$ coordinate at which the two lines intersect.

As computers have become more and more powerful, the use of artificial intelligence has become ever more prominent in modern computing. As a result, a mechanism called a neural network has become a very commonly used tool for replicating the basic biological processes that result in the function of the brain. Neural Networks are composed of a series of "layers" of nodes, where each node of layer $$$i$$$ will connect with every node of layer $$$i+1$$$.

When an object is rotating around a central point in circular motion, a force called centripetal force exists. Centripetal force is the force that pulls the object towards the center, preventing it from flying off in a straight line. An equation exists to relate the centripetal force $$$F_c$$$, the mass of the object $$$m$$$, the tangential velocity $$$v$$$, and the radius of the circle $$$r$$$. This equation is represented as follows: $$$F_c = \frac{mv^{2}}{r}$$$. To solve this problem, you will be given the centripetal force, the mass of the object, and the radius of the rotation. With this information, determine the tangential velocity of the moving object.

When trading securities such as stocks and crypto-currencies in the markets, many traders look at mathematical tools called indicators. There are hundreds of different indicators for all sorts of purposes, but one of the most commonly used indicators is called the relative strength index, or RSI for short. The RSI provides an estimate of how the price of a security is likely to move, with a high RSI value(above 70) suggesting the item is overpriced and will decrease in value, while a lower value(below 30) suggests the opposite. The RSI is calculated with a simple formula that is based on the past prices of a security. This formula is given as: $$$100-(100/(RS+1))$$$ where $$$RS = aveUP/aveDOWN$$$. $$$aveUP$$$ is the average value among all of the times the price of the security increased between two measurements, and $$$aveDOWN$$$ is the average value among all of the times the price of the security decreased between two measurements. For this problem, take in the past $$$N$$$ prices of an asset, then determine the value of the RSI indicator. It is important to note that aveDOWN should be composed of the absolute value of each price decrease between two measurements, and therefore should have a positive value.

Bob is attempting to encrypt information so that only those he trusts with the secret code can decode his secret information. Instead of using a highly secure encryption method, bob uses a method called rotation, where he shifts each letter of his phrase a certain number of characters up or down. This shift works by moving the character up and down the alphabet, so the character 'a' shifted by 5 would become 'f'. A shift also wraps around the alphabet, so if you were to shift 'a' by -5, it would become 'v'. In addition, a character can be shifted by values greater than 26, so for example 'a' shifted by 30 would become 'e', wrapping all the way back around the alphabet. To solve this problem, you will be given a single lowercase string and a series of rotations, with each rotation corresponding to the character in the string with the same index. Perform each rotation on each character and determine what the resulting string would be.

As you may know, large prime numbers are in very high demand currently, and there are many large scale searches for even larger primes. Some of the largest prime numbers discovered fit a number called a Mersenne Prime, which is essentially any prime number than can be represented by the equation $$$2^{p}-1$$$. Mersenne Primes are especially interesting as they can be tested for primality with a special test called the Lucas-Lehmer test. Although you could technically solve Mersenne Primes using typical prime-number algorithms, the Lucas-Lehmer test will almost always be faster. The pseudocode for conducting the Lucas-Lehmer test for as found on Wikipedia is as follows:

In a previous contest, a question was asked about determining how many days apart two dates were, ignoring leap years. This question is essentially the same, except it includes leap years. In addition, this question only asks for the count of days from $$$date 1$$$ to $$$date 2$$$, and $$$date 2$$$ will always be after $$$date 1$$$. Take in two dates in the form of month-name day-number, year. Then print out the number of days from the first date to the second one, and make sure that your calculation includes the addition of days added by leap years.

Given the three points that represent the corners of an isosceles triangle, determine the angle that the triangle is pointing. The angle can be calculated based on the vector created along the line of symmetry of the triangle that exits through the point of the triangle. The angle should be represented in degrees and should be determined relative to the vector (1,0). The following image shows a triangle with points at (-1,0), (0,1), and (-2,2), and has an angle of 135 degrees.

For the first problem, we'll keep it simple to make sure you understand how this format works.

You have acquired the Infinity Gauntlet from Thanos from the Marvel Universe. For those who are unfamiliar with the Infinity Gauntlet, it contains immense power with the ability to many things, but most notably, to reduce numbers into half.

You've been selected to be the recipient of Wegman's shopping spree program! The only caveat is that you have to be continuously moving through the building at all times, through the different sections in a circular pattern, so you will only have time to grab one item from each section. It will also take some time for you to move to the different locations of the store, and luckily, this Wegmans only has 3 sections, as the architect designing this location was lazy with his design.

You want to know how many loops it will take you to get a certain amount of different types of items.

Getting back from the grocery store, you bought a whole bag of candies just for you to eat. You put the candy in a jar, and hide it in your room. Unfortunately, you notice that the number of candies in the jar are going down each day, but you do not know by how much.

You want to know how much the thief has stolen every day.

You are an event organizer, tasked with planning an event in a very large, outdoors area. However, you only have two very powerful speakers, which are placed on both ends of the stage.

You assume that there will be crowds spanning large lengths at this meeting, and need to figure out how long it takes for the sound from the stage to reach the furthest attendees of the event.

However, an engineer helping to organize the event reminds you that the speed of sound is varied, depending on the temperature. As you are planning the event in Syracuse, this is a serious problem, as the temperatures are very unpredictable.

The approximate formula for the speed of sound (assuming there is no humidity in the air, is):

$$$V = (331.3 + .606∙\vartheta)$$$

Where $$$V$$$ is the speed of sound in meters per second, and $$$\vartheta$$$ is the temperature of the air, in degrees Celsius.

Throughout this global pandemic, many health experts and doctors are steadfast on the effort to "flatten the curve", or to decrease the maximum amount of people who are getting infected by the virus, using the method of social distancing, one of the reasons why we are in quarantine at this very moment.

The daily rate of infection, if left unchecked, can look a lot like this logistic function, where $$$\Delta N$$$ is the total number of cases, $$$\Delta t$$$ is the time period for new infections, (which, in this case, would be one day.)

$$$\frac{\Delta N}{\Delta t} = a(1-\frac{N}{N_{max}})N$$$

$$$a$$$ is the infection rate, which, for COVID-19, would be .394 (with social distancing, the number is able to go down). Finally, $$$N_{max}$$$ is the total amount of infections we can expect for the curve to flatten. In this simulation, we will calculate the total number of days $$$t$$$ the virus will take in order for it to infect the entire population of America dependant on its infection rate, which will be about 320 million people.

A color wheel is a tool used to determine the relationships of different colors, often by the distance between two colors on the wheel.

Using the given simple color wheel above, your task is to determine the shortest numerical distance between two colors.

Leet, (also known as 1337 sp34k or Elite Speak), was a prominent use of letter swapping during early internet culture.

Set types of letters would be able to be substituted for different numbers which would have similarities to the letters they were replacing. For this basic translator, only these conversions are needed:

a = 4 b = 8 e = 3 i = 1 l = 1 o = 0 s = 5 t = 7 z = 2

You have an in-home library, but its organization is a mess! Fantasy books next to non-fiction biographies, detective novels next to ancient classics, and worst of all, the author's names aren't in alphabetical order!

To fix this problem, you decide to create a program that is able to divide the books into different genre groups, with the authors of the genres listed in alphabetical order.

The FBI has been working hard to find the location of a criminal organization by analyzing their use of repeating patterns in sections of their internal communications. So far, this process has been entirely manual and is therefore slow, so you are tasked with creating a program to automate this pattern finding. Determine whether or not a section of text repeats a single string multiple times. The problem is that you don't know what string it is that is being repeated, though you do know that the pattern will always begin immediately. A pattern will always appear as the same string being repeated at least twice. It is also important to note that there can be unimportant text that follows the repetition that is not a part of the pattern. All of this following text should be ignored. It is also important to note that the repeated string must be at least two characters.

The Octal Numeral system is a Base-8 number system, with the same concept and algorithm as other number systems, such as binary and hexadecimal. The advantages of using the base 8 system, is that all of its components are made of numbers, unlike the hexadecimal system, and is shorter than the binary system.

On a regular acoustic guitar, the open (regular) strings are tuned with these notes, starting from lowest to highest:

E-A-D-G-B-E

You can change these values into different notes using the tuning pegs on the top of the guitar, twisting it forwards or backwards to change the pitch of the strings. One full rotation of the peg would be equivalent changing the pitch by one semitone, or a half step in pitch. For instance, using the piano keys up above, F would move up to F#, or if moved down a semitone, would be moved down to an E.

When given certain note values, your job is to tune the song based on how many semitones you are given. This is known as transposing.

Though you may have completed the previous task to analyze and find patterns in sections of text, the FBI has realized that it needs a more powerful program that is able to find more complex patterns and with more constraints. Your new program should be able to identify if a repetition pattern exists within a string regardless of where it starts. You will also be supplied with a number that represents how many repeats there should be. Your program should only output "True" if the number of repetitions precisely matches the number provided.

Bob has an array of integers, and Bob is curious whether or not his array is symmetrical on two axis of symmetry. Write a program that takes in an array of integers and outputs whether or not the array is symmetrical. The two axis of symmetry are the horizontal and the vertical. It is important to note that if an odd number of columns or rows is present, the middle row and/or column(s) should be considered the axis and should be completely ignored in the symmetry analysis. Integers are considered symmetrical if they are the same value across an axis of symmetry. Your program should only output "True" if the array is symmetrical on both the horizontal and vertical axis of symmetry.

Welcome to the CodeRams Contest #8, and thanks for participating!

We like to make contests with themes that tie together all of the problems. For this contest, the problems are all based on songs by the German band Kraftwerk. We'll provide links to each of the songs in each corresponding problem. We recommend that you listen to each song while you are solving each problem. (You're allowed to view the provided links, despite them requiring use of the internet.)

The Robots (the song corresponding to this problem)

For this first problem, you want to train your robot army to print out a given string of text three times.

Radioactivity

You're trying to determine how many neutrons are in a certain radioactive isotope. You know how many protons are in the isotope, and you know the isotope's mass number. The mass number of an isotope is defined as the number of protons plus the number of neutrons. Given the number of protons and the mass number, figure out how many neutrons are in the radioactive isotope.

The Model

You are making a model airplane, which will be powered by rubber bands. Luckily, to speed up the process of winding the rubber bands, you have a crank winder, which has a certain ratio (e.g. 15:1), representing how many winds of the rubber band one turn of the winder will result in. Given this value, and how many winds you ultimately want the airplane's rubber band to have, figure out how many times you need to turn the winder.

Computer World

You just bought a new computer, and you wonder if it has a large, medium, or small amount of storage on its hard drive. The storage of your computer's hard drive will be given in gigabytes (GB).

If your computer's storage space is less than or equal to 200 GB, you consider it SMALL.

Otherwise, if your computer's storage space is less than or equal to 500 GB, you consider it MEDIUM.

Otherwise, you consider it LARGE.

Given these storage space bounds, figure out whether or not your computer's storage is SMALL, MEDIUM, or LARGE, and print the answer accordingly.

Spacelab

With the CodeRams club, you've created a lab in space to study solar power. You created your lab on a planet in our solar system. Unfortunately, a rival CodeQuest team also created a spacelab on a different planet. You need to figure out which spacelab is closer to the sun.

For reference, the order of the planets in our solar system from closest to farthest away from the sun is "Mercury", "Venus", "Earth", "Mars", "Jupiter", "Saturn", "Uranus", "Neptune" (you can copy this into a list/array if you want).

The Telephone Call

You want to call Lockheed Martin to register your team for CodeQuest 2021, but you don't know their phone number. However, you know some of the digits of the phone number. You're going to try to call all possible phone numbers, given the digits that you know, and you want to know how many numbers you're going to have to call. For this problem, assume that all area codes are valid.

Music Non Stop

You're trying to find the longest possible piece of music, so that you can play music non-stop. Given a list of songs and their durations (in MM:SS, with leading zeros), figure out which song is the longest.

Computer Love

You love your computer, and you want to give it a present: a large integer. However, your computer especially loves powers of two. Given two numbers $$$x$$$ and $$$y$$$, find the largest power of two between $$$x$$$ and $$$y$$$, i.e. find the largest number $$$n$$$ such that $$$x$$$ <= $$$n$$$ <= $$$y$$$, and $$$n$$$ is a power of two.

Techno Pop

After listening to the Kraftwerk song Techno Pop, you decide that you want to pop a balloon. You have a spherical balloon that will pop when it reaches a volume of $$$v1$$$ in^3, and you blow up the balloon inside of a cube-shaped box with a volume of $$$v2$$$ in^3.

Given these values, figure out whether or not it is possible to pop the balloon in the cube-shaped box that you have.

Recall that the formula for the volume of a sphere is $$$\frac{4}{3}\pi{}r^3$$$, where $$$r$$$ represents the radius of the sphere, and the formula for the volume of a cube (or a cube-shaped box) is $$$s^3$$$, where $$$s$$$ represents the side length of the cube.

Numbers

You're working with large numbers, and you want to calculate the totient function of a certain one. The totient function of a number $$$n$$$ is defined as the number of positive integers less than or equal $$$n$$$ that are relatively prime with $$$n$$$, i.e. the number of integers $$$k$$$ such that $$$k$$$ <= $$$n$$$ and $$$gcd(k, n) = 1$$$.

For example, the totient of $$$15$$$ is $$$8$$$, because 1, 2, 4, 7, 8, 11, 13, and 14 are relatively prime with $$$15$$$, while 3, 5, 6, 9, 10, 12, and 15 are not. 4 is relatively prime with 15, because there aren't any common factors of 4 and 15. 4 has factors {2}, and 15 has factors {3, 5}. On the other hand, 10 is not relatively prime with 15, because 10 and 15 both have a common factor of 5.

Given an integer $$$n$$$, figure out the value of $$$φ(n)$$$, where $$$φ$$$ represents the totient function as described above.

Neon Lights

You are trying to find strings of text to put on neon lights. You want to fully test the extent of the neon lights' writing style for letters, so you want to pick the string of text that has the highest number of distinct (different) letters from a selection of possible strings of text.

It's More Fun To Compute

You are trying to discover that it's more fun to compute, and you're doing so by evaluating long strings of text. You define the fun-ness of a string to be the amount of characters in the string that are equal to "f", "u", and "n". You can perform cyclic shifts on the string an infinite number of times. When you cyclically shift the string, each character changes into the one after it, so any "a" characters become "b", "b" becomes "c", etc. "z" characters turn into "a" in a cyclic shift.

Given that you can perform an infinite number of cyclic shifts on the input string, find the maximum fun-ness of the string.

Autobahn

You are about to drive on the Autobahn. You have several different cars, and you're trying to decide which one to take on the Autobahn. The different cars have differing fuel efficiencies, measured in miles per gallon (MPG), and the cars have different top speeds. You calculate a car's score as its fuel efficiency (MPG) multiplied by its top speed.

Given the list of possible cars, your task is to sort them by their score.

Ohm Sweet Ohm

You have a circuit consisting of many resistors in parallel, and you want to calculate their equivalent resistance, in ohms.

If you competed in our Contest #2 back in January, you might remember that the formula for calculating the equivalent resistance of two resistors in parallel with resistances $$$a$$$ and $$$b$$$ is $$$(a * b) / (a + b)$$$.

To calculate the equivalent resistance of three parallel resistors, first calculate the equivalent resistance of the first two using the formula described above. Then, use the formula again to calculate the equivalent resistance of the third resistor and the value you just calculated, the equivalent resistance of the first two resistors. Calculating the equivalent resistance of more than three resistors works in a similar way.

Formally, the equivalent resistance of $$$n$$$ resistors can be calculated by plugging in the equivalent resistance of the first $$$n - 1$$$ resistors, and the resistance of the $$$n$$$th resistor, into the above formula.

Metropolis

You're driving through a metropolis. The metropolis can be represented as a 2D grid of buildings, each with a height value between $$$0$$$ and $$$9$$$. You consider a building to be a skyscraper if it has a greater height than all of the buildings directly adjacent to it (including diagonally). Given this 2D grid of building heights, figure out which buildings are skyscrapers, and which ones aren't.

Pocket Calculator

You have a pocket calculator. Unfortunately, it is broken, so you need to calculate large math operations yourself. For this problem, you need to write a computer program to calculate the answer to a long math operation, with multiplication (denoted by an asterisk *), division (denoted by a slash / ), addition, and subtraction. There will not be parentheses or exponents. Recall order of operations: multiplication and division (with equal weight) from left to right first, followed by addition and subtraction (with equal weight) from left to right. Using eval() or similar commands for this problem is not allowed.

Home Computer

You are programming your home computer. You want your computer to learn Calculus, so today you decide to write a computer program to calculate the derivative of a polynomial function.

The derivative of a "power function" $$$x^n$$$ is defined as $$$nx^{n-1}$$$. For example, the derivative of $$$x^5$$$ would be $$$5x^4$$$.

The derivative of a constant multiple of a power function $$$kx^n$$$ is defined as $$$knx^{n-1}$$$. For example, the derivative of $$$3x^4$$$ would be $$$12x^3$$$.

When taking the derivative of several terms added or subtracted to each other, you take the derivative of each term individually. For example, the derivative of $$$3x^5 - 5x^4$$$ would be $$$15x^4 - 20x^3$$$.

The "power rule" described above works intuitively if all terms have at least a degree of two (the number that $$$x$$$ is taken to the power of). For terms with a degree of one, such as $$$7x$$$, the derivative is just the constant multiple in front of $$$x$$$, which is $$$7$$$ for this example. For constant terms (with a degree of zero), the derivative is zero, and can be cancelled out.

Using this knowledge, your task is to write a program to determine the derivative of a given polynomial function.

Trans Europe Express

You're traveling on the Trans Europe Express, which consists of many train lines between cities. You want to know how many cities you can reach from a given start city, traveling only on the Trans Europe Express.

For example, if you started in City A, and the Trans Europe Express had train lines between City A and City B, City B and City C, and City D and City E, you could travel to City B or City C, but not to City D or City E.

For problems like these, you can use the graph theory algorithm Breath-First Search (BFS). The algorithm is described below in pseudocode:

1. Define an empty list of cities. Add the start city to the list.

2. Select the first city in the list of cities, and remove it from the list.

3. Mark the selected city as visited

4. For any edges that connect the selected city to another city, add the other city to the list of cities, if the city has not been visited yet

5. If the list of cities is not empty, repeat steps 2-4.

Then, the answer would be the number of cities that have been visited.

Planet of Visions

You are trying to test your vision using an eye test chart, and you want to see if you have 20/20 vision or not. You attempt read the text on the chart, and you unfortunately get some of them wrong. Now, you're curious how close you were to correctly reading the text.

You consider some pairs of letters similar. For example, "D" and "P" look relatively similar from far away. Given the letter pairs that you consider to be similar to each other, your task is to figure out how many of the letters you got right, how many you were close on (the letters were similar), and how many you got completely wrong (the letters were not similar). Note that letters are also similar to letters that its similar letters are similar to. For example, if "D" and "P" are similar, and "D" and "G" are similar, "P" and "G" are by definition similar as well.

Geiger Counter

You're in a large maze, and unfortunately the maze is filled with differing amounts of uranium ore, which could potentially expose you to dangerous amounts of radioactivity. Luckily, you have brought your trusty Geiger Counter with you, so you can measure the radioactivity of any given part of the maze in counts per minute (CPM).

You start at the top left corner of the maze, and you are trying to travel to the bottom of the maze. For any path through the maze, its radioactivity value is defined as the maximum CPM across all cell in the maze that you travel through on the path. Your task is to find the path through the maze with the lowest radioactivity value, in other words, find the highest CPM you have to expose yourself to if you travel on the optimal path.

You're allowed to move in any direction (except diagonally), and you can visit the same cell twice (although it is never necessary to).

Note that since the constraints on the size of the maze are fairly large, a brute force (complete search) solution that tries all possible paths,will not work.

The Man Machine

You played against a Man Machine in chess, and because it is a superhuman being, you lost every game. Now, you're trying to practice chess so that you can beat the Man Machine.

To practice, you want to figure out how many different ways there are to place $$$N$$$ queens on an $$$N$$$ by $$$N$$$ chessboard, such that no two queens attack each other (queens can attack any number of spaces directly diagonal, left, right, up, or down). This is called the $$$N$$$-queens problem, and is a standard computer science problem involving recursion and backtracking. Your task is to implement this solution on chessboards where $$$N$$$ can be up to 9.

The Hall Of Mirrors

You are in a hall of mirrors, and you shine a laser beam in a certain direction. Given the position of several diagonal mirrors, figure out the path of the laser beam.

You shine your laser beam from the back of the hall of mirrors (on a computer screen, this will look like the "bottom" of the image).

Drawn an H. You will be given a number the represents the length of the legs and middle portion of the H.

Much like the previous question, you are going to be making some ASCII art. In this question your job is to make a pyramid given a number that represents the base of the pyramid. Each layer going up from the base should be 2 less in length than the previous layer. The pyramid is complete when the length of the top layer is either 1 or 2.

In this question you must encrypt or decrypt a message by replacing a key letter with a word or a key word with a letter. If the message contains the key word then you should be decrypting and replacing the key word with the key letter. If the message given does not contain the key word then you should be encrypting and should be replacing the key letter with the key word. The key letter will not be within the key word.

Converting from one unit of measurement to another is very useful. Make a program that can convert between, feet, inches, meters, centimeters, miles, and kilometers. Use the following conversions to get the correct answer: .08333 feet in 1 inch, 3.28084 feet in 1 meter, 0.0328084 feet in one centimeter, 5280 feet in 1 mile, and 3280.84 feet in 1 kilometer.

You're flying an airplane, but you forgot to forgot to refill the fuel tank before you trip. Therefore, you must decide which airport to land at based on a number of factors: proximity, available runway space, and direction. If an airport has no available spaces, you cannot go there. If an airport is too far away, you cannot go there.

So I think the title explains it. Encrypt a given phrase using the vigenere cipher with a key that will be provided. The vigenere cipher is actually quite easy to use, just look at the image below. The left side is where the plain text characters go and the top is where the key letters go. The first letter of the plain text goes with the first letter of the key and all you do is draw a line across for the plain letter and a line down for the key letter. Where the two lines intersect is the new encrypted letter. Then you pair the second letter of the plain text with the second letter of the key and so on. Once you have reach the last letter of the key, you just go to the start of the key again. Also don't encrypt spaces, so just skip over them.

In this question your goal is to make a program that will simulate running some pretty basic pseudocode. Here is the syntax that will be used:

Defining a variable: -"var variableName = value" -value can be any integer -value can be a simple math equations ex: "3 + 5" -value can be a simple math equation that includes a variable "testVar + 2"

Manipulating a variable: -"variableName = value" -same rules applied to what the value can be as the one above -Ex: "test1 = test1 + 2 - test2"

Printing: -"print (hello word )+exampleVariable+" -text that is being printed will be surrounded in parentheses -variables being printed will be surrounded in addition signs

You consider a string to be a diverse string if every pair of adjacent characters are different. For example coderams is a diverse string, while hello is not.

Given a string, figure out whether or not it is a diverse string.

You have a list of $$$n$$$ books. You want to read one complete book, but you want to read as few pages as possible. You're given the list of how many pages each book has. Figure out the minimum number of pages that you have to read, reading at least one complete book.

In computer graphics, colors are often given as three integers $$$R$$$, $$$G$$$, and $$$B$$$, each ranging from 0 to 255, inclusive.

When displaying a bright red color, $$$R$$$ = 255, $$$G$$$ = 0, and $$$B$$$ = 0.

When displaying a bright green color, $$$R$$$ = 0, $$$G$$$ = 255, and $$$B$$$ = 0.

When displaying a bright blue color, $$$R$$$ = 0, $$$G$$$ = 0, and $$$B$$$ = 255.

When displaying a bright yellow color, $$$R$$$ = 255, $$$G$$$ = 255, and $$$B$$$ = 0.

Given this information, figure out which color corresponds to a RGB-format color given in the input.

You recently performed well in an online Codeforces contest, and you became part of "Division 1" on Codeforces. However, you're not sure that it will last. If you have a rating of 1900 or higher you're considered Division 1, otherwise, you're considered Division 2.

In each contest after you became Division 1, you didn't perform very well. Thus, your rating will decrease by 50 in each contest. Given your start rating, figure out how many contests it will take for you to become Division 2.

For example, if your start rating was $$$1970$$$, your rating would be $$$1920$$$ after the first contest, and after the second contest your rating would be $$$1870$$$, and you would become Division 2.

Your 5-year-old cousin from the CodeRams Contest #5 (Problem 4) is now in 4th grade, and he is learning how to simplify fractions. Unfortunately, he doesn't really understand them, and he needs your help in simplifying fractions.

For this problem, you must write a program to convert a fraction $$$a$$$/$$$b$$$ to simplest form. For example, if the fraction was $$$6$$$/$$$8$$$, you can factor out a $$$2$$$, and the fraction simplifies to $$$3$$$/$$$4$$$, which is in simplest form.

You're traveling through space in your spaceship, when your ship's radar detects several hostile aliens near the ship. You need to figure out how close each alien is to your ship.

In three dimensions, the distance between two points, each with an X, Y, and Z coordinate, is defined as follows:

Given the coordinates of your ship, in 3D space, figure out how far away each alien is from your ship, using the formula described above.

You're phone has incorrectly autocorrected some of your recent texts, and you're trying to make a more effective autocorrect system.

You're given an incorrectly spelled word. The similarity index of two words $$$s$$$ and $$$t$$$ is calculated as follows:

1. Define two variables: $$$tot$$$, representing the total pairs checked, and $$$mat$$$, representing the matches found.

2. Iterate through all pairs of letters in $$$s$$$ and $$$t$$$.

3. Increment $$$tot$$$ by one, and if the letters are equal, increment $$$mat$$$ by one as well.

The similarity index is calculated as mat / tot.

Given several words, your autocorrect system will choose the word which is the most similar to the original word, using the algorithm described above.

You're trying to come up with a good Codeforces username. You want to use something similar to your real name, but not exactly your real name, to not release too much info about yourself online. Thus, you decide to encode your username using an Affine cipher.

An affine cipher uses a key of two values: $$$a$$$ and $$$b$$$. Given a letter $$$l$$$, you first convert it into it's "character code", for example, "a" would become $$$0$$$, "b" would become $$$1$$$, etc. We'll call this $$$x$$$. Then, you calculate the value of $$$a$$$$$$x$$$ + $$$b$$$ mod $$$26$$$, and reverse the character code mapping that you used previously, to convert the answer back into a letter. The affine cipher runs this process on all letters (not spaces) in a given string.

For example, let's use the letter $$$c$$$, and a key of $$$a$$$ = $$$15$$$, and $$$b$$$ = $$$5$$$. $$$c$$$ has a character code of $$$2$$$. Then, the encoded character has a character code of $$$15$$$*$$$2$$$ + $$$5$$$ mod $$$26$$$ = $$$35$$$ mod $$$26$$$ = $$$9$$$. Thus, the encoded character is $$$j$$$.

You attended the final stage of the Tour De France, and after the event has ended, you want to know the final results. However, all you know is how long it took each biker to reach your position, and how fast they were traveling when they passed you.

Given your constant position during the race, the position of the finish line, and the information described above, you must figure out the final standings of the race. You can assume that after each biker passed you, they maintained a constant speed.

You're listening to music, and you hear a major chord of three notes. You want to figure out which chord you just heard.

In music, the notes in a single octave, from lowest to highest, are as follows: C, C#, D, D#, E, F, F#, G, G#, A, A#, and B. Any two adjacent notes in this list are a "half step" apart. For example, C and D differ by 2 half steps, and A and D differ by 5 half steps.

Additionally, notes can be represented as both sharps and flats. For example, C# and D ♭ (D flat) are the same note, and D# and E ♭ are the same note. A flat note will be represented with a lowercase f in the input, such as "Df" for D flat.

A major chord has a $$$root$$$, a $$$third$$$ note, and a $$$fifth$$$ note. The root and the third note must differ by exactly four half steps, and the third and fifth note must differ by exactly three half steps. Correspondingly, the root and the fifth note must differ by exactly seven half steps.

Given this information, and a major chord, figure out what the root of the chord is. The notes of the chord can be given in any order, i.e. the root doesn't necessarily come first.

You're going to a city that has a large subway system. The subway system has $$$n$$$ lines, and each line has a certain number of stations. However, some stations are "transfer stations": multiple lines go through them.

Given a list of the stations that each subway line goes through, your task is to figure out how many transfer stations exist throughout the subway system.

Note that "loop lines" that start and end at the same station may appear in the input, and stations that are the start and end of the loop but have no other lines going through them do not count as transfer stations. For a station to be a transfer station, it has to have multiple distinct lines going through it.

A latin square is defined as a 4 by 4 grid of numbers, where all of the numbers in each row and column are distinct, i.e. no two pairs of elements in each row and column are equal.

You're given a partially filled in latin square. Figure out how many valid latin squares can be formed by filling in the empty digits of the latin square.

Your 5-year-old cousin from the CodeRams Contest #5 (Problem 4) is now in 4th grade, and he is learning how to add fractions. Unfortunately, he doesn't really understand them, and he needs your help in adding two or more fractions together.

For this problem, you must write a program to add several positive fractions together.

Since the test cases can be large, you will need to use an efficient method to solve it.

When adding two fractions together, you first change the denominators into their LCM (least common multiple).

The LCM of two numbers $$$a$$$ and $$$b$$$ can be calculated using the following formula:

LCM($$$a$$$, $$$b$$$) = $$$\frac{a * b}{GCD(a, b)}$$$, where GCD represents the greatest common divisor of $$$a$$$ and $$$b$$$.

You can find the greatest common divisor (GCD) or $$$a$$$ and $$$b$$$ efficiently using the following recursive algorithm:

1. If $$$a$$$ is less than $$$b$$$, swap $$$a$$$ and $$$b$$$

2. If $$$b$$$ is equal to $$$0$$$, return $$$a$$$

3. Otherwise, return GCD($$$b$$$, $$$a$$$ mod $$$b$$$)

You're play a modified version of Conway's Game of Life on a 2D grid. Each cell on the grid can be represented as three states:

An asterisk, representing a cell that is "alive"

A period, representing a cell that is "dead"

An uppercase X, representing a "barrier".

On each turn, cells change their state depending on the following rules:

1. If the cell is not a barrier and is adjacent to any dead cells, the cell becomes a dead cell

2. If the cell is a barrier, is adjacent to only barriers, and is not on the edge of the board, it becomes a dead cell

Note that in these definitions, "adjacent to" refers to all 8 of the spaces next to a cell, including diagonally. Also note that all of the changes to cells take effect after the current turn, so the order that you apply the operations in doesn't matter.

It can be shown that if played infinitely many times, this (simplified) version of Conway's Game of Life will eventually converge on a single board state, i.e. the board will eventually never change between turns. Given a starting board, figure out the final state of the board if played infinitely many times.

You're playing Minecraft, and having fun exploring your world in Creative mode. Your world consists of Desert, Forest, and Taiga biomes.

You've explored some of the world, but not all of it. Thus, for some places, you know their biome, and for others, you don't. The world is given as a 2D top-down view, with some spaces ("chunks") unknown, and others with a known biome.

You especially like Taiga biomes. You've already explored at least one space that is a taiga biome, and you know that your world has exactly one taiga biome. Given this information, your task is to figure out the maximum amount of spaces (chunks) on the 2D world map that can be part of a taiga biome, and which spaces could potentially be part of the taiga biome.

Two spaces are considered part of the same biome if you can travel on the 2D grid from one space to the other, traveling on only spaces of the given biome. For example, if two spaces are both in Taiga biomes, but to travel from one to the other you are forced to cross a desert, they are not part of the same biome.

If you competed in the CodeRams Contest #8, you might remember a problem involving mirrors and light. This is a more difficult and updated version of that problem.

You are in a hall of mirrors, and you shine a laser beam in a certain direction. Given the position of several diagonal mirrors, figure out the path of the laser beam.

You shine your laser beam from the back of the hall of mirrors (on a computer screen, this will look like the "bottom" of the image).

This problem also adds "star blocks", which shine light in all directions when light passes through them.

You have a function $$$f(x)$$$, and you want to figure out how the area under $$$f(x)$$$ from 0 to $$$C$$$.

In calculus, this value is called the $$$integral$$$ of $$$f(x)$$$. For some functions, taking its integral is relatively easy and uses a few simple rules. However, for many functions, it is impossible to find their integral exactly. However, you can make an approximation of the integral, and since you're writing a computer program, you can make a close approximation.

One way to approximate the integral of a function is to use the Rectangular Approximation Method, or RAM. This method approximates the function $$$f(x)$$$ as $$$n$$$ rectangles, each having an equal width, and having varying $$$y$$$-values depending on the value of $$$f(x)$$$ at that point.

As you can see, the example with $$$n$$$=4 ($$$f(x)$$$ was divided into four rectangles) was not perfect. However, as $$$n$$$ gets larger and larger, the approximations get more and more accurate.

Formally, define the LRAM (Left Rectangular Approximation Method) approximation of the area under a function $$$f(x)$$$ from $$$0$$$ to $$$C$$$, using $$$n$$$ rectangles, as A, and the area of each rectangle as A1, A2 ... AN, as the following:

A = $$$\frac{A1 * C}{N}$$$ + $$$\frac{A2 * C}{N}$$$ + $$$\frac{A3 * C}{N} $$$+ ... + $$$\frac{AN * C}{N}$$$.

The area of each rectangle can be calculated using the standard formula A = $$$l$$$ x $$$w$$$. The width of each subrectangle is equal to $$$\frac{C}{n}$$$ (because there are $$$n$$$ rectangles with a total width of $$$C$$$). The length of each subrectangle is equal to $$$f(\frac{k * c}{n})$$$, where $$$k$$$ represents the index of the rectangle, ranging from $$$0$$$ to $$$n - 1$$$, inclusive.

Since your answer must be a relatively close approximation, but your program should fit inside of the 10 second time limit (longer than usual for this problem), you should set $$$N$$$ equal to 50000.

You consider a string to be a question if its last character is a question mark. Given a string, figure out whether or not it is a question.

You define a string to be an alarming string if it contains exactly three "a" characters. Given a string, possibly containing spaces, figure out whether or not it is an alarming string.

You're given a list of $$$n$$$ words. You've discovered that when a rival CodeQuest team finds a list of words, they sort it in alphabetical order. To distinguish yourself from your rival CodeQuest team, you decide to sort the list of words in reverse order.

You're competing in a large individual math team contest. In the contest, you're given several sets of problems, and for each one of them you get a certain number of them correct. Given this information, you want to figure out your total score in the competition.

For example, if you scored a 2 out of 3 on the first problem set, and a 3 out of 5 on the second problem set, your total score would be 5 out of 8.

You consider a number to be cheesy if it is divisible by the sum of its digits. For example, the sum of the digits of 360 is 9, and 360 is divisible by 9, so 360 is a cheesy number. On the other hand, the sum of digits of 87 is 15, and 87 is not divisible by 15, so 87 is not a cheesy number.

Given a number $$$n$$$, figure out whether or not it is a cheesy number.

A number is considered a perfect number if and only if the sum of its divisors, except for the number itself, is equal to the original number. For example, 28 is a perfect number because its divisors are $$$1$$$, $$$2$$$, $$$4$$$, $$$7$$$, and $$$14$$$, and $$$1$$$ + $$$2$$$ + $$$4$$$ + $$$7$$$ + $$$14$$$ = $$$28$$$.

Given an integer $$$n$$$, figure out whether or not it is a perfect number, and what the sum of its divisors (except for $$$n$$$) is.

Your computer outputs $$$n$$$ integers randomly. You think it might be a secret code, so you decide to make a list of the numbers, but maintain the list in sorted order as you add each number.

For example, if the computer output was $$$3$$$ $$$4$$$ $$$2$$$ $$$8$$$ $$$7$$$, you would first add $$$3$$$ to the list, making the list [3].

Then, you would add $$$4$$$ to the list, making the list [3, 4].

Then, you add $$$2$$$, putting it first in the list to maintain the list's sorted order. The list becomes [2, 3, 4]

The process proceeds until the list is [2, 3, 4, 7, 8] after the final step.

You're eating at a continental breakfast in a hotel, and there are two menu options. Each menu option consists of several food items. You want to find how many food items are contained in both menus.

You define a string to be a majestic string if each successive character in the string comes one character later in the alphabet than the one before it. For example, bcdef is a majestic string, and so is xyz, but acd is not a majestic string. The characters also wrap from z to a, so yzab is a majestic string.

Given a string $$$s$$$, figure out whether or not it is a majestic string, using the rule described above.

You have a tree that is growing very fast. At first, the tree has one branch. On each successive day, the tree grows a certain number of branches. On each day, the number of new branches is calculated as $$$n$$$ times $$$b$$$, where $$$b$$$ represents how many branches were on the tree on the previous day, and $$$n$$$ is a variable you have to calculate. $$$n$$$ will always be greater than one.

At an unknown number of days, the tree has $$$x$$$ branches. Given this value, figure out the minimum possible value of $$$n$$$ used in the formula, given that the tree started out with exactly one branch.

You're attending an international Zoom call during the Coronavirus quarantine, where the attendees represent many different countries. The zoom call is really long, and to pass the time, you tally how many people are from each country.

Given the list of people and their countries, print the countries, and how many meeting attendees are from each country. Sort the countries first by their number of attendees, and if two countries have an equal number of attendees, sort them alphabetically by the name of the country.

You have a triangle with three points given in coordinates. Given this information, figure out the triangle's area. The points can be given in any order.

To calculate the area of a triangle, you can use Heron's Formula, which is described below:

Define $$$A$$$, $$$B$$$, and $$$C$$$ to be the lengths of the three sides of the triangle.

Define $$$S$$$ to be equal to $$$\frac{A + B + C}{2}$$$.

Then, the area of the triangle is calculated as $$$\sqrt{S(S - A)(S - B)(S - C)}$$$.

You've traveled across a galaxy far, far away, and you land on a planet with two different alien species. Each alien species counts numbers in a different base. Aliens of the first species count numbers using base $$$a$$$, and aliens of the second species count numbers using base $$$b$$$. The base used by most humans is decimal, base 10.

The two alien species are about to start a war, because they cannot properly communicate in numbers. Your task is to convert a number from the first alien species, in base $$$a$$$, into base $$$b$$$, in order to avert the impending alien war.

You're standing in a large 2D grid. The grid consists of several gold blocks. The gold is highly sought after , so for each position in the grid you want to calculate how many steps it would take to walk to the nearest gold block. You can walk left, right, up, or down, but not diagonally.

This is a sigificantly harder version of a previous problem in the contest. We recommend you solve the earlier problem first.

You're given the coordinates of an $$$n$$$-sided polygon. The polygon is not necessarily a regular polygon (the sides and angles are not necessarily equal), but the polygon is guaranteed to be convex (the polygon will not contain any angles greater than or equal to 180 degrees).

Given this information, figure out the area of the given polygon.

You have a string, consisting of at most seven characters, not including spaces. You want to find all of the anagrams of the string. A string $$$t$$$ is defined as an anagram of a string $$$s$$$ if an only if the characters of $$$s$$$, in sorted order, not including spaces, are equal to the characters of $$$t$$$, in sorted order, not including spaces.

You're also given a dictionary of $$$n$$$ words.

An anagram is considered a valid anagram if it consists of only space-separated words that are in the dictionary. For example, if the dictionary was the English dictionary, hello and hello world would be valid anagrams, but he llo and helloworld would not be valid anagrams.

Given the string, and the dictionary, print all of the valid anagrams of the string, in alphabetical order.

For this problem, you will be given two side lengths of a triangle and will be required to determine the length of the other side. You can assume that all input will be provided for a valid right triangle. The two side lengths you will be given correspond to the common variables $$$A$$$ and $$$C$$$, meaning one side and the hypotenuse. You should then output the length of side $$$B$$$.

Your task for this problem is to take the three side lengths of a triangle and to determine if these side lengths could create a "valid" triangle. A triangle is considered valid if the addition of any two side lengths is less than the length of the other side, in other words, the following must evaluate to true: a+b>c, a+c>b, b+c>a.

For this problem, you will be asked to solve specified trigonometry problems. You will be given individual problems that contain sin,cosine,tangent,cosecant,secant, and cotangent. Each test case will specify which operation should be used, using the following keywords: "sin,cos,tan,cosec,sec,cotan". Each test case will also provide the value that should be input into the various trigonometry functions. Your program should output the result of each computation.

The Unit Circle is a very commonly used geometric representation of all possible right triangles with a hypotenuse length of one. If you have not yet encountered the unit circle in math class, the coordinates of each point on the circumference of the circle can be found simply by finding the sin and cosine of the angle created between the point and (0,0). The x value can be found as the cosine of the angle while the y value can be found as the sin of the angle. For this problem, you will be given the angle(from 0 to 359), and you should output the x value.

Though digital communications are highly accurate, errors can occur from time to time. To deal with such communications errors, methods to detect and fix errors have been invented. One very common and simple method for this is known as a parity bit. When a message is being sent digitally in the form of bytes of 8 bits, a ninth parity bit can be added that is either 1 if the message has an even number of 1s(in binary), or 0 if the message has an odd number of 1s. While this method clearly will only work if there are an odd number of errors, it is a useful heuristic for detecting many errors without the need for more computation intensive methods. Your task for this problem is to write a program to determine if a nine bit sequence of binary is valid according to a parity check. The first bit on the left represents the parity bit, and the following 8 bits correspond to the one byte message that is to evaluated for parity.

Binary Coded Decimal(BCD) is a method of representing a value with binary notation while using the same digit places as base 10(decimal). For example, the value 783 in decimal translates to 1100001111 in standard binary, though it would instead translate to 011110000011 in binary converted decimal. This BCD converted value is composed of three chunks of 4 bits each, where each 4-bit chunk corresponds to a different digit from 783. While BCD is not used as commonly in software development, it is critical in 7-segment display systems. These circuits display a multi-digit number by splitting it into its individual digits, then sending each individual digit to a different display, creating the image of an entire number with multiple digits. Your task for this problem will be to take a base-ten decimal and to convert it into a BCD value. Each base-10 digit should be represented by four binary digits, and the individual chunks should be concatenated together to produce the final output.

For this task, you will be required to find a set of simple statistics based on a given set of data. Data will be provided as an array of integers, and you will be tasked with finding the mean, median, mode, and range of the data.

For this problem, you will be tasked with sorting a series of houses by how close they are to a given house. The rules for house distances are as follows: houses on the same street will have have a distance of the difference between their house numbers, and houses on different streets will experience a distance equal to the difference between their house numbers times the difference between their street numbers. Houses will be each provided with a unique name, such as "h1", and will also have a street number that represents which street they live on as well as a house number that represents their position on the street. For this problem, you will be given a series of houses and their respective values and you will need to determine which house is the closest to a specified house. For example, you may be given h1,h2,h3,h4,h5, then asked to find the closest house to h3.

While the equation of sin is highly stressed in high school math class, the methods for computing the sin of any input algebraically is usually not explained. There are various methods that can be used by computers or by hand, though the Taylor Approximation and CORDIC methods are most common. Calculators use CORDIC for its high speed and accuracy, though this problem will cover the Taylor Approximation method. If you have not yet had experience with calculus or the Taylor series, a Taylor Approximation is essentially a way to represent a function as a series of polynomial expressions. The use or details of this concept is not relevant to the question, though it is important to not that a Taylor Series will approximation its original function. In the case of the sin operation, the Taylor Approximation can be found as $$$x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \frac{x^9}{9!}...$$$ The pattern can be repeated continuously to increase the accuracy of the approximation, and the approximation will only work on smaller radian values of input. In addition, if you have not seen the $$$!$$$ operator before, it is known as the factorial. The factorial of a number can be computed as the number multiplied by each integer below it, so $$$3! = 3*2*1 = 6$$$. For this problem, you will be provided with number of terms to use for the Taylor Approximation along with a radian angle value for input into the equation. You should then output the approximation for sin of this input value using the given number of terms of the Taylor Approximation.

For this problem, you will be tasked with finding the dot product of two given matrices. Dot products are a very common matrix operation, and find uses in many fields of math, computer science, and physics. If you haven't had any experience with a matrix in the past, think of matrices as a "table" of values, similar to a multi-dimensional array. Matrices can be of any dimension, yet this problem will only focus on two dimensional matrices. The result of a dot product operation on two matrices m1 and m2 in the form m1*m2 will result in a matrix with the same number of rows as m1, and the same number of columns as m2. It is difficult to explain the computation of the dot product in text, so here is an image representing it:

Pascal's Triangle is a famous concept in mathematics, and it has proven to have incredible relevance in many fields of mathematics even hundreds of years after its creation. The triangle is very simple to construct, starting out with just the number one centered on the first line of a sheet of paper. On the second line, write two ones centered just to the left and right of the one above. For any given line on the triangle, a value is found by adding the value to the upper right and upper left of the specified point, even if the upper right or upper left doesn't exist(meaning the specified point is on the edge of the triangle). Values on the edge of the triangle will always be 1. Your task for this problem is to find the maximum value on a given line of pascal's triangle(with the top line being 0).

Ken Ken is a number puzzle created in 2004 by Tetsuya Miyamoto.

You're solving Ken Ken puzzles from a puzzle book. Each puzzle is an $$$n$$$ by $$$n$$$ grid, and you have to fill in all of the spaces in the grid.

There are also $$$k$$$ "freebie" spaces, which have already been filled in.

Given $$$n$$$, the size of the grid, figure out how many total spaces you have to fill in. For example, to solve a 4 by 4 puzzle with two freebies, you would have to fill in 14 spaces.

After the end of hair salon restrictions of quarantine, many clients come to get their hair cut. Naturally, after months of uncut hair, your client's hairdos can be quite long! Your clients all have a preference of how long their hair needs to be after it is cut, and you can measure how long their hair is once you start cutting their hair.

You must determine how much hair you have to cut in order to reach the specified length of hair the client requested.

Your younger sibling needs help with their algebra homework, and it involves a full worksheet of detecting parallel lines in equations! Too inarticulate to explain how to find these parallel lines, you decide to create a piece of code that will solve the problems for them.

A "FizzBuzz" question is a standard interview question given to any computer science job applicants that tests the applicant's aptitude to solve and code basic problems, including the style they program in. A shocking fact, but many entry level computer science graduates do not know how to practically code, and this question is able to filter out the applicants that do not have the ability to program out of a simple question.

Given two numbers, $$$x$$$ and $$$y$$$, print out the numbers in between these two numbers, $$$x$$$ (inclusive) and $$$y$$$ (exclusive), but if the number is a multiple of 3, replace the printed number with the string, "Fizz", and if the number is a multiple of 5, replace the printed number with the string, "Buzz". If the number is a multiple of both 3 and 5, replace the printed number with the combination of the two strings, "FizzBuzz".

You are working as a cashier for a supermarket, and items are handed to you to be scanned one by one by the customer. You do not know how many items they have, but after the last item is scanned, the customers usually say, "done".

While doing your gym assignments in quarantine, your gym teacher makes you record your heart rate after your workouts, and separates them into five "zones". These zones of fitness are sorted dependant on your maximum heart rate (MHR), which is determined by taking your age, and subtracting it from 220.

The zones are separated thusly:

Zone 5: 90 - 100 percent of MHR

Zone 4: 80 - 89 percent of MHR

Zone 3 : 70 - 79 percent of MHR

Zone 2 : 60 - 69 percent of MHR

Zone 1 : <60 percent of MHR

Over the quarantine season, you decide to watch your weight by limiting yourself to a certain amount of calories a day. In your house, you stocked up on a small variety of foods before the quarantine, and regardless of what time of the day it is, you must choose from these items:

Steak: 500 Cal

Apple: 100 Cal

Bread: 50 Cal

In the card game of blackjack, a player competes with a dealer, who in the first rounds, distributes two cards to both the player, and to themselves. These two cards determine the play of the next turn, as the objective of the game is to achieve a total score of 21, through the combination of number and face cards.

Each face card is worth 10 points, while the number cards are worth their value points in their numbers. An ace, however, is worth 11 points, but if an ace causes the player's pool to go over its 21 point limit, it may become devalued to 1 point.

First envisioned by the French mathematician, Blaise Pascal, Pascal's Triangle is a formation of numerals that are arranged in such a way that a number composing a part of the triangle is the summation of the adjacent binomial pair of the previous row in the triangle.

Morse code, developed in 1837, along with the invention of the telegram, was a revolutionary invention that struck a new frontier in the subject of telecommunications. Through a series of electrical pulses, messages could be sent to far distances through a series of dots and dashes, and at a speed that was unheard of before its invention. Since then, telegrams and Morse code have been essential in the realm of communications, especially in its role in the military, where fighter pilots were required to memorize Morse code until the 1990s.

Your job is to create a translator that will take in messages encode it in morse, and output the result in alphabet form.

Every morning after you get out of bed, you brew yourself a nice cup of coffee to get yourself ready for the day. However, most of the time when you pick up the coffee to drink, it's too hot for you to drink! You know that Newton's Formula of Cooling is $$$T(t) = T_{s} + (T_{0} - T_{s})e^{-kt}$$$, where:

$$$T(t)$$$ is the temperature of the coffee at time $$$t$$$,

$$$T_{s}$$$ is the ambient temperature of the room,

$$$T_{0}$$$ is the initial temperature of the coffee, and

$$$k$$$ is the decay constant.

You also know that the coffee reaches your favorable heat from a initial temperature of 210 degrees to 120 degrees after 15 minutes of cooling, in a room temperature of 70 degrees.

A number is called a palindrome if it reads the same forwards and backwards. For example, 5775, 98389, 7, and 66 are palindromes, but 552, 35, and 86867 are not palindromes.

Given a number $$$n$$$, figure out the closest $$$k$$$ palindromes to $$$n$$$. If two palindromes have the same distance away from $$$n$$$, print the smaller one first.

For example, let's say $$$n$$$ = 600 and $$$k$$$ = 4.

The closest palindrome to $$$n$$$ is 595, with a distance of 5. The next closest palindrome is 606, with a distance of 6. The next two are 585 (distance of 15) and 616 (distance of 16), so we would print 595, 606, 585, and 616, in that order.

You're tired of the warm July weather, so you and your friends decide to take a trip to Antarctica, and have a snowball fight.

Each person is given a very large number of snowballs (essentially, an infinite number). Each person is also wearing a coat with a certain color, and boots with a certain color.

Throughout the snowball fight, each person throws their snowballs at everyone else who doesn't either have the same color of coat, or the same color of boots, exactly once. Obviously, people don't throw snowballs at themselves.

Given this information, figure out how many snowballs are thrown in total during the snowball fight.

There have been a lot of online Codeforces contests recently.

On Codeforces, each user is given a rating, which is a positive integer less than 4000. After each worldwide contest (which 10000+ users compete in on average), everyone's rating value increases or decreases, depending on their performance in the competition. The higher your rating, the higher rank you will need to get a positive rating change. For example, if a user had a rating of 3700, their rating could decrease if they got 2nd place in a contest (out of 10000+ people). On the other hand, if a user was rated 900, their rating would increase even if they came in 5000th or 6000th place (out of 10000). As a result of this formula, the list of the top 10 users on Codeforces (based on rating) is constantly changing, although one person is usually at #1.

You're given a list of $$$n$$$ codeforces users, and their rating before any of the recent contests. You're then given a list of $$$k$$$ contests. Each contests contains the rating change for each contestant. Given this information, your task is to print out the list of the top 10 highest rated users after each contest.

You're traveling through space, but unfortunately, your spaceship has a limited amount of fuel. There are $$$n$$$ planets that you want to travel to on your journey through space, and each planet can be represented by an $$$x$$$, $$$y$$$, and $$$z$$$ coordinate.

You start on Earth, which can be represented as the origin (0, 0, 0) on the 3D coordinate plane. You want to find the minimum distance you can travel, if you start on Earth, visit all of the planets at least once, and end on Earth.

Recall that to calculate the distance between two points in 3D space, you can use the distance formula:

Over the quarantine season, you decide to watch your weight by limiting yourself to a certain amount of calories a day.

In this problem, you're given the number of calories of each food item in your house as input.

You want to figure out the minimum number of food items that you need to eat in order to have eaten exactly $$$n$$$ calories.

You're testing out a catapult that you built for POE class, and you're trying to get it to launch an eraser over a wall.

The catapult launches the eraser $$$a$$$ meters away from the wall, and you're trying to get the catapult to hit a target $$$b$$$ feet above the ground, and $$$c$$$ meters away from the wall in the exact opposite direction.

The wall is $$$d$$$ meters high, and it is very thin (assume it has no thickness).

Given this information, figure out the minimum possible maximum height of the eraser, such that the eraser still clears the wall. In other words, among all eraser trajectories that hit the target and successfully clear the wall, find the lowest possible maximum height of the eraser.

Assume that you launch the device in a vacuum (i.e. there is no air resistance).

Ken Ken is a number puzzle created in 2004 by Tetsuya Miyamoto.

Like Sudoku, Ken Ken involves placing numbers into an n by n grid, and it requires each row and column to contain distinct integers from 1 to n. n can range from 4 to 7, inclusive.

Additionally, each of the n * n cells in the Ken Ken puzzle is assigned to a "cage" consisting of one or more cells. If a cage consists of multiple cells, they have to form a single block of cells connected vertically or horizontally, but not diagonally. For example, an L-shaped cage, or a 2 by 2 square cage would be valid, but a cage consisting only of two cells at the opposite end of the board would not be valid. Usually, cages don't have more than 4-5 cells (although there is no upper limit).

For each cage in the puzzle, if it consists of only one cell, the cage will simply be assigned a number, indicating which number is placed in the cage in the final solution. This is called a "freebie".

Otherwise, each cage with two or more cells is assigned a math operation. All of the cells in the cages must complete the math operation successfully. For example, if a cage had the operation "9+", the total sum of the numbers in the cells of the cage would have to sum to 9. If a cage had the operation "120x", the total product of the numbers in the cage would have to be 120.

Cages can also have subtraction or division operations. These types of cages have to have exactly two cells. For subtraction, the difference of the two numbers in the cage must equal the given number. For example, if a cage had the operation "2-", then the numbers could be 3 and 1, in any order. They could also be 4 and 2, 2 and 4, 5 and 3 (if the board was at least 5 by 5), and so on. Cages with division work similarly. The number in the cage must equal the quotient of the higher number divided by the lower number. For example, for a "2/" cage, the numbers could be 1 and 2, or 2 and 1, or 4 and 2, and so on. As such, the required number of a cage will always be a positive integer.

Note that although all rows and columns must consist of distinct numbers, cages do not have to.

Here's an example of what an unsolved Ken Ken puzzle looks like:

And here's the solution to the same Ken Ken puzzle:

Your task, as you might have guessed, is to write a program to solve a Ken Ken puzzle. All of the Ken Ken puzzles will range from 4 by 4 to 7 by 7 in size, and they will all be taken from a book of Ken Ken puzzles, meaning that they will all be potentially solvable by a human.

Good luck!