HMMT 二月 2000 · 团队赛 · 第 8 题
HMMT February 2000 — Team Round — Problem 8
题目详情
- A w oman has $1.58 in p ennies, ni k els, dimes, quarters, half-dollars and silv er dollars. If she has a di eren t n um b er of oins of ea h denomination, ho w man y oins do es she ha v e? 4
解析
- If she has a silv er dollar, then she w ould ha v e to o man y other oins, as 0 half dollars, 2 quarters, 3 dimes, et . w ould b e greater than the total. So she has no silv er dollars, and at least one of ev ery other denomination. Con tin uing, it turns out the only feasible solution is 0 silv er dollars, 1 half dollar, 2 quarters, 3 dimes, 4 ni k els, 8 p ennies, for a total of 18 oins. 4 4