HMMT 二月 2000 · 团队赛 · 第 10 题
HMMT February 2000 — Team Round — Problem 10
题目详情
英文原题
- Ho w man y times p er da y do at least t w o of the three hands on a lo k oin ide?
解析
英文解析
- The se ond hand rosses the min ute hand 59 times an hour. The se ond hand rosses thehour hand 60 times an hour, ex ept for 2 of the hours, due to the mo v emen t of the hourhand. The min ute hand and the hour hand ross 22 times total, be ause the hour handompletes 2 rotations in a da y , and the min ute hand ompletes 24. The se ond, hour,
and min ute hand all oin ide only at no on and midnigh t, but we'v e oun ted each ofthese 12:00's 3 times instead of on e. Therefore, the answ er is 59 60 + 60 24 2 + 22 2 2,
giving us 2872 rossings. m