Track / Stage 5 / 39 of 400 #639 of 1964

Problem 639

AIME late

Combinatorics Difficulty 5.1 Find the answer

The ninety-ninth question: Given that $\mathrm{n}$ is a positive integer, find the smallest positive integer $\mathrm{k}$ such that in a $2 \mathrm{n} \times 2 \mathrm{n}$ grid, marking $\mathrm{k}$ cells ensures there is a unique way to tile the $2 \mathrm{n} \times 2 \mathrm{n}$ grid with $1 \times 2$ and $2 \times 1$ dominoes, with no domino containing two marked cells.

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Official solution

None

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None

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.