HMMT 十一月 2015 · 冲刺赛 · 第 1 题

HMMT November 2015 — Guts Round — Problem 1

[ 5 ] Farmer Yang has a 2015 × 2015 square grid of corn plants. One day, the plant in the very center of the grid becomes diseased. Every day, every plant adjacent to a diseased plant becomes diseased. After how many days will all of Yangs corn plants be diseased?

解析

[ 5 ] Farmer Yang has a 2015 × 2015 square grid of corn plants. One day, the plant in the very center of the grid becomes diseased. Every day, every plant adjacent to a diseased plant becomes diseased. After how many days will all of Yangs corn plants be diseased? Proposed by: Alexander Katz Answer: 2014 After k minutes, the diseased plants are the ones with taxicab distance at most k from the center. The plants on the corner are the farthest from the center and have taxicab distance 2014 from the center, so all the plants will be diseased after 2014 minutes.