A — Captcha
Author: m7a1g5i8k8a1r4p0
Just print the number of circles in the image. There are 7 if you include the circles in i and ?.
B — Right or Wrong?
Author: m7a1g5i8k8a1r4p0
The title implies that you should check if the 3 numbers are "right" or not. You can do this by checking that $$$a$$$, $$$b$$$, and $$$c$$$ form the side lengths of a right triangle, with $$$c$$$ as the hypotenuse.
C — New Sorting Algorithm
Author: ChiMasterBing
You are sorting a permutation, so all you have to do is print out the integers from $$$1$$$ to $$$n$$$, inclusive. The time constraints are very lax for this. Though you should be careful of the memory limit. If you read the second line entirely, you will probably get MLE. If you form a large string and then print it out, you will probably get MLE.
D — Subset Sums
Author: m7a1g5i8k8a1r4p0
Clearly, solving this problem as is is too hard. Is there anything that you are missing here?
Try pressing Ctrl+A to highlight all the text.
If you highlight the space below "Notes," you will see the following equations: 
If you plot these functions in Desmos, you will realize that $$$a$$$ is still a variable. By setting $$$a$$$ to $$$0$$$, $$$1$$$, and $$$2$$$, you will see the equations spell out XOR.
This signifies that the question is actually asking about how many subset XOR sums equal $$$k$$$. This can be done in $$$O(n\log \max{a_i})$$$
E — Gemini
Author: m7a1g5i8k8a1r4p0
To solve Castor's Problem, all even numbers must be put into separate sets. It can be shown that the required number of sets is always equal to $$$\lfloor\frac{n}{2}\rfloor$$$
