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2022 Combo Div 2 P3

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February 28, 2022
combinatorics

Problem Statement

We say that a set SS of 33 unit squares is commutable if S={s1,s2,s3}S = \{s_1,s_2,s_3\} for some s1,s2,s3s_1,s_2,s_3 where s2s_2 shares a side with each of s1,s3s_1,s_3. How many ways are there to partition a 3×33\times 3 grid of unit squares into 33 pairwise disjoint commutable sets?
Proposed by Srinivasan Sathiamurthy
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