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#189 Going back in time

Set by Steve Wain

My 24-hour LED clock has a six-digit display that shows hours, minutes and seconds. I have noticed that this sometimes means I get palindromic times – those that read the same backwards and forwards (starting at 00:00:00 of course).

The other day, I looked at the clock and the time was a palindrome. In less than 10 minutes, it happened again! Within an hour of that, I looked at the clock again. Another palindrome. But I then had to wait for what turned out to be the equal longest possible gap before the next palindrome turned up. A similar long gap had happened earlier in the day.

What time was it when I first looked at the clock?

Solution next week

#188 Four forgetful footballers

Solution

Interlecht were the champions.

The results for each team were three of 3-0, 2-1, 1-2 and 0-3, and the four teams’ total goals must have been six, five, four or three in some order. The teams that scored six and five goals both won two games and lost the other; the highest/lowest-scoring teams won/came bottom of the table on goal difference. Cleverton lost 3-0 to Smarta Prague and must have ended bottom. Astutegart weren’t bottom, so must have won a game 3-0, and it must have been against Smarta Prague. Interlecht are the only team who didn’t lose a game 3-0, so were the top- scoring team – hence champions.