疯狂时钟
Crazy Clock
题目详情
一只“疯狂时钟”有两根指针，初始都指向 12。
在一段时间内：
- 分针顺时针转了 5 圈回到 12（速度可变）。
- 同时，时针逆时针转了 4 圈回到 12（速度可变）。
问：两根指针相互穿过（相遇并越过，忽略起点与终点重合）多少次？
There is a crazy clock in Alice's Dream, it has two hands initially pointing at 12. The minute hand moves clockwise, making 5 rounds (with varying speeds) and comes back to 12. In the same time, the hour hand goes anti-clock wise, finishing 4 rounds and returns to 12. How many times did the two cross each other ? (Cross means meet & pass through, hence ignore start & end)
解析
答案是 8 次。
在分针参考系中，时针相对分针一共逆时针转了 圈。
每完成一圈必与分针相遇一次，但起点与终点不计，因此相遇次数为 。
Original Explanation
8
Solution
In the reference frame of minute hand, hour hand moves exactly (5+4) = 9 rounds anti-clockwise with varying speeds (by adding total angular distance covered). 'Cross' occurs just in between two consecutive rounds. Thus hour hand crosses minute hand exactly 9-1=8 times. Same answer in ref. plane of hour-hand.