2022 SSMO Relay Round 5 Problems
Problem 1
Consider an chessboard with a knight in one of the center squares. The knight may move in an -shaped fashion, going two squares in one direction and one square in a perpendicular direction, but cannot go outside the chessboard. How many squares can the knight reach in exactly two moves?
Problem 2
Let TNYWR, and let be a sequence of 2022 positive integers such that and . Also, for all . Find the number of possible sequences .
Problem 3
Let TNYWR, and let $a_k=\cis\left(\frac{k\pi}{T+1}\right)$ (Error compiling LaTeX. Unknown error_msg). Suppose that can be expressed in the form of , where $\cis(x) = \cos(x) + i\sin(x)$ (Error compiling LaTeX. Unknown error_msg). Find .