Problem 1

Evie is hosting a birthday party in which she has the most important job: sharing the cake. She invited 6 guests, and noticed that she could slice everyone including herself a piece with only 4 straight cuts (see picture below). This made her wonder about the following question: if she were to make exactly 2025 straight cuts, with each cut going from edge to edge and bisecting the cake entirely, how many different possible values are there for the numbers of pieces she can end up with?

(For example, with 2 straight cuts, she could either cut the cake into three or into four pieces, so the answer would be 2.)

To deter guessing without thinking, we ask that you also solve the following simple arithmetic problem before checking your answer:

What is 9 + 5 + 5?

This problem was first solved on Wed 22nd January at 4:17:45pm