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Problem 1059

AMC 12 late, AIME early

Combinatorics Difficulty 5.0 Find the answer HMMT February

Call the pentominoes found in the last problem square pentominoes. Just like dominos and ominos can be used to tile regions of the plane, so can square pentominoes. In particular, a square pentomino tiling of a region of the plane is a way of covering it (and only it) completely by nonoverlapping square pentominoes. How many square pentomino tilings are there of a 12-by-12 rectangle?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Since 5 does not divide 144, there are 0.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.