HMMT 十一月 2022 · GEN 赛 · 第 1 题
HMMT November 2022 — GEN Round — Problem 1
题目详情
- Emily’s broken clock runs backwards at five times the speed of a regular clock. Right now, it is displaying the wrong time. How many times will it display the correct time in the next 24 hours? It is an analog clock (i.e. a clock with hands), so it only displays the numerical time, not AM or PM. Emily’s clock also does not tick, but rather updates continuously.
解析
- Emily’s broken clock runs backwards at five times the speed of a regular clock. Right now, it is displaying the wrong time. How many times will it display the correct time in the next 24 hours? It is an analog clock (i.e. a clock with hands), so it only displays the numerical time, not AM or PM. Emily’s clock also does not tick, but rather updates continuously. Proposed by: Brian Liu, Luke Robitaille, Selena Liu Answer: 12 Solution: When comparing Emily’s clock with a normal clock, the difference between the two times decreases by 6 seconds for every 1 second that passes. Since this difference is treated as 0 whenever 12 it is a multiple of 12 hours, the two clocks must agree once every = 2 hours. Thus, in a 24 hour 6 period it will agree 12 times.