HMMT 二月 2002 · 冲刺赛 · 第 18 题
HMMT February 2002 — Guts Round — Problem 18
题目详情
英文原题
- [ ± 5] Call the pentominoes found in the last problem square pentominoes . Just likedominos and ominos can be used to tile regions of the plane, so can square pentominoes. Inparticular, a square pentomino tiling of a region of the plane is a way of covering it (and onlyit) completely by nonoverlapping square pentominoes. How many square pentomino tilingsare there of a 12-by-12 rectangle?
a 3
解析
英文解析
- Call the pentominoes found in the last problem square pentominoes . Just likedominos and ominos can be used to tile regions of the plane, so can square pentominoes. Inparticular, a square pentomino tiling of a region of the plane is a way of covering it (and onlyit) completely by nonoverlapping square pentominoes. How many square pentomino tilingsare there of a 12-by-12 rectangle?
Solution: Since 5 does not divide 144, there are 0 . a