Difference between revisions of "2022 SSMO Relay Round 5 Problems"
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Revision as of 21:59, 31 May 2023
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
.