HMMT 二月 2003 · 冲刺赛 · 第 22 题

HMMT February 2003 — Guts Round — Problem 22

个人笔记

[9] There are 100 houses in a row on a street. A painter comes and paints every housered. Then, another painter comes and paints every third house (starting with housenumber 3) blue. Another painter comes and paints every fifth house red (even if itis already red), then another painter paints every seventh house blue, and so forth,
alternating between red and blue, until 50 painters have been by. After this is finished,
how many houses will be red?

解析

There are 100 houses in a row on a street. A painter comes and paints every house red.
Then, another painter comes and paints every third house (starting with house number