HMMT 二月 2002 · 冲刺赛 · 第 18 题
HMMT February 2002 — Guts Round — Problem 18
题目详情
- [ ± 5] 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? 3 a
解析
- 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? Solution: Since 5 does not divide 144, there are 0 . a