MathDB
Odd Tilings

Source: EGMO 2022/5

April 9, 2022
CombocombinatoricsEGMOEGMO2022

Problem Statement

For all positive integers nn, kk, let f(n,2k)f(n, 2k) be the number of ways an n×2kn \times 2k board can be fully covered by nknk dominoes of size 2×12 \times 1. (For example, f(2,2)=2f(2, 2)=2 and f(3,2)=3f(3, 2)=3.) Find all positive integers nn such that for every positive integer kk, the number f(n,2k)f(n, 2k) is odd.
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