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HMMT 二月 2001 · 冲刺赛 · 第 46 题

HMMT February 2001 — Guts Round — Problem 46

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ ± 5] Draw a rectangle. Connect the midpoints of the opposite sides to get 4
    congruent rectangles. Connect the midpoints of the lower right rectangle for a total of 7
    rectangles. Repeat this process infinitely. Let n be the minimum number of colors we canassign to the rectangles so that no two rectangles sharing an edge have the same color and mbe the minimum number of colors we can assign to the rectangles so that no two rectanglessharing a corner have the same color. Find the ordered pair ( n, m ).
解析

英文解析

  1. [ ± 5] Draw a rectangle. Connect the midpoints of the opposite sides to get 4
    congruent rectangles. Connect the midpoints of the lower right rectangle for a total of 7
    rectangles. Repeat this process infinitely. Let n be the minimum number of colors we canassign to the rectangles so that no two rectangles sharing an edge have the same color and mbe the minimum number of colors we can assign to the rectangles so that no two rectanglessharing a corner have the same color. Find the ordered pair ( n, m ).
    Solution: (3 , 4) .