## Teaser 2972: A relaxing day

**From The Sunday Times, 8th September 2019** [link]

George and Martha have a digital clock, which displays time with six digits on the 24-hour system (i.e. HH:MM:SS).

One afternoon, George looked at the clock and saw a six-digit display involving six different positive digits. He dozed off immediately, and when he awoke in the evening he saw another display of six digits, again all positive and different. He dozed off immediately and later on (before midnight) he awoke, having slept for exactly 23 minutes longer than the previous time. At that time, he saw a third display, yet again six different positive digits. He thus had seen eighteen digits and the nine positive digits had each appeared exactly twice.

At what time did George wake up after his first sleep?

[teaser2972]

## Jim Randell 6:30 pm

on6 September 2019 Permalink |This Python program looks for possible 6-digit times composed of different digits, it separates them into afternoon (before 6pm) and evening (after 6pm) and the looks for two times in the evening that have a difference that is 23 minutes longer than the difference between the first time and one of the afternoon times. We then check the three times between them use each of the digits exactly twice. It runs in 460ms.

Run:[ @repl.it ]Solution:After the first nap George awoke when the clock read 19:56:48.There are two possible start times for the first nap (although they are within a minute of each other), but in both cases the wake time from the first nap is the same, and so there is a unique answer to the puzzle.

The two possible sequences are:

And these are the only two sequences even if we don’t restrict the first time to be “afternoon” and the final two times to be “evening”.

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## GeoffR 3:33 pm

on10 September 2019 Permalink |LikeLike