HMMT 十一月 2015 · 冲刺赛 · 第 13 题
HMMT November 2015 — Guts Round — Problem 13
题目详情
英文原题
- [ 9 ] Consider a 4 × 4 grid of squares, each of which are originally colored red. Every minute, Piet canjump on one of the squares, changing the color of it and any adjacent squares (two squares are adjacentif they share a side) to blue. What is the minimum number of minutes it will take Piet to change theentire grid to blue?
解析
英文解析
- [ 9 ] Consider a 4 × 4 grid of squares, each of which are originally colored red. Every minute, Piet canjump on one of the squares, changing the color of it and any adjacent squares (two squares are adjacentif they share a side) to blue. What is the minimum number of minutes it will take Piet to change theentire grid to blue?
Proposed by: Alexander Katz
Answer: 4
Piet can change the colors of at most 5 squares per minute, so as there are 16 squares, it will takehim at least four minutes to change the colors of every square. Some experimentation yields that it isindeed possible to make the entire grid blue after 4 minutes; one example is shown below:
XXXX
Here, jumping on the squares marked with an X provides the desired all-blue grid.