a fly in a 1995 x 1995 chessboard
Source: : I Soros Olympiad 1994-95 Ukraine R2 9.3 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics
June 6, 2024
combinatorics
Problem Statement
Given is a square board measuring . These cells are painted with black and white paints in a checkerboard pattern, so that the corner cells are black. A spider sitting on one of the black cells can crawl to the cell on the same side as the one it occupies in one step. Prove that a spider can always reach a fly sitting motionless in another black cell by visiting all the cells of the board once.