HMMT 二月 2002 · 冲刺赛 · 第 16 题
HMMT February 2002 — Guts Round — Problem 16
题目详情
- [5] Divide an m -by- n rectangle into mn nonoverlapping 1-by-1 squares. A polyominoof this rectangle is a subset of these unit squares such that for any two unit squares S, T inthe polyomino, either
英文原题
[5] Divide an m -by- n rectangle into mn nonoverlapping 1-by-1 squares. A polyomino
of this rectangle is a subset of these unit squares such that for any two unit squares S, T in
the polyomino, either
(1) S and T share an edge or
(2) there exists a positive integer n such that the polyomino contains unit squares
S 1 , S 2 , S 3 , . . . , S n such that S and S 1 share an edge, S n and T share an edge, and for all
positive integers k < n , S k and S k +1 share an edge.
We say a polyomino of a given rectangle spans the rectangle if for each of the four edges
of the rectangle the polyomino contains a square whose edge lies on it.
What is the minimum number of unit squares a polyomino can have if it spans a 128-by-
343 rectangle?
解析
英文解析
- Divide an m -by- n rectangle into mn nonoverlapping 1-by-1 squares. A polyomino ofthis rectangle is a subset of these unit squares such that for any two unit squares S, T in thepolyomino, either