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Tiling with 6 types of tiles

Source: 2023 Israel TST Test 3 P1

March 23, 2023
TilingcombinatoricsTST

Problem Statement

Toph wants to tile a rectangular m×nm\times n square grid with the 66 types of tiles in the picture (moving the tiles is allowed, but rotating and reflecting is not). For which pairs (m,n)(m,n) is this possible?
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