HMMT 二月 2000 · GEN 赛 · 第 19 题
HMMT February 2000 — GEN Round — Problem 19
题目详情
- Elev en pirates nd a treasure hest. When they split up the oins in it, they nd that there are 5 oins left. They thro w one pirate o v erb oard and split the oins again, only to nd that there are 3 oins left o v er. So, they thro w another pirate o v er and try again. This time, the oins split ev enly . What is the least n um b er of oins there ould ha v e b een?
解析
- Let y b e the n um b er of oins in the hest. F rom the problem, w e kno w that y 5 (mo d 11), y 3 (mo d 10), and y 0 (mo d 9). Com bining these giv es us that y 423 (mo d 990), so the answ er is 423 . 2 5 25