# Sunday Times Teaser 2972 – A Relaxing Day

*by Danny Roth*

#### Published September 8 2019 (link)

George and Martha have a digital clock, which displays time with six digits on the 24-hour system, ie 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?

I tried a permutation solution for this teaser, but it was taking too long to find a solution. Brian assisted me in speeding up the code to a more reasonable run-time.