**Hello Codeforces!**↵
↵
I would like you guys to invite in this dc server, I ~Hardik120710,2026-08-31 is one of the mods in the server and ~amnxd,2026-08-31 is the server owner.↵
↵
The server is very active! People discuss problems on Codeforces Contests, Atcoder, Codechef, etc.↵
↵
Whether you are a absolute beginner or an absolute master the server is open for everyone!↵
↵
Server is also open for Math Enthusiasts!↵
↵
As a gift from $Benevolent$, here is a easy combinatorial problem↵
↵
<a href="https://discord.gg/FWJkxTxZH">Server Invite</a>↵
↵
<spoiler summary="Problem">↵
↵
**Aaradhya** was hired by Eiffel 65 to design a strong password for a lock for the concert hall at **Blue Galaxy**. The password has $n$ digits and each digit can take values from 0 to 9. The password has the following properties:↵
↵
Let $D_i$ denote the $i$-th digit of the password.↵
Note: $D_1$ can be 0.↵
↵
- $D_1 < D_2 > D_3 < \dots$ that is the digits are alternating.↵
- $|D_i - D_{i-1}| \geq k$ for all $i$ from 2 to $n$. That is the absolute difference between two digits is atleast $k$ where $k \geq 1$.↵
↵
For a given length $n$ and minimum absolute consecutive difference of digits $k$ how many passwords **Aaradhya** can create (generalize)?↵
↵
↵
</spoiler>↵
↵
<spoiler summary="Solution">↵
↵
Join the $Benevolent$ discord server to get solutions and more problems!↵
↵
Till that, enjoy **I'm Blue** by **Eiffel 65**↵
↵
<a href="https://imgbb.com/"><img src="https://i.ibb.co/4ZDSP0V4/Blue-da-ba-dee-by-EIFFEL-65-online-video-cutter-com.gif" alt="Blue da ba dee by EIFFEL 65 " border="0"></a>↵
↵
</spoiler>↵
↵
Even orz people like ~fatespeaker,2026-08-31 is in the discord server too!↵
↵
↵
I would like you guys to invite in this dc server, I ~Hardik120710,2026-08-31 is one of the mods in the server and ~amnxd,2026-08-31 is the server owner.↵
↵
The server is very active! People discuss problems on Codeforces Contests, Atcoder, Codechef, etc.↵
↵
Whether you are a absolute beginner or an absolute master the server is open for everyone!↵
↵
Server is also open for Math Enthusiasts!↵
↵
As a gift from $Benevolent$, here is a easy combinatorial problem↵
↵
<a href="https://discord.gg/FWJkxTxZH">Server Invite</a>↵
↵
<spoiler summary="Problem">↵
↵
**Aaradhya** was hired by Eiffel 65 to design a strong password for a lock for the concert hall at **Blue Galaxy**. The password has $n$ digits and each digit can take values from 0 to 9. The password has the following properties:↵
↵
Let $D_i$ denote the $i$-th digit of the password.↵
Note: $D_1$ can be 0.↵
↵
- $D_1 < D_2 > D_3 < \dots$ that is the digits are alternating.↵
- $|D_i - D_{i-1}| \geq k$ for all $i$ from 2 to $n$. That is the absolute difference between two digits is atleast $k$ where $k \geq 1$.↵
↵
For a given length $n$ and minimum absolute consecutive difference of digits $k$ how many passwords **Aaradhya** can create (generalize)?↵
↵
↵
</spoiler>↵
↵
<spoiler summary="Solution">↵
↵
Join the $Benevolent$ discord server to get solutions and more problems!↵
↵
Till that, enjoy **I'm Blue** by **Eiffel 65**↵
↵
<a href="https://imgbb.com/"><img src="https://i.ibb.co/4ZDSP0V4/Blue-da-ba-dee-by-EIFFEL-65-online-video-cutter-com.gif" alt="Blue da ba dee by EIFFEL 65 " border="0"></a>↵
↵
</spoiler>↵
↵
Even orz people like ~fatespeaker,2026-08-31 is in the discord server too!↵
↵
