快猫短视频

#190 All square

Set by Zoe Mensch

The secretary of my tennis club has just changed the six-digit code for the padlock at the entrance gate. 鈥淎s a mathematician, you will be interested to know that the new code is a square number,鈥� he said.

鈥淩eally?鈥� I replied, only mildly interested.

鈥淭he code is also the final score of the three-set league match I played last week.鈥�

鈥淎nd you have other clues to help me?鈥�

鈥淣o, that鈥檚 it,鈥� he said. And he was right. After a few 鈥渁ha鈥� moments, I narrowed the possibilities to a small range, and with the aid of a calculator discovered that there is only one 鈥減roper鈥� three-set tennis result that is a square. Can you find it?

(A reminder of tennis scoring: the first person to win six games with a lead of two games wins the set, such as 6-3 or 6-4. However, if it goes to 5-5, the first to 7-5 wins; and if it goes to 6-6, there is a tie-break, the victor of which wins the set 7-6. First to win two sets wins the match and the eventual winner鈥檚 games are always published first. If the score was 7-6, 2-6, 6-3, the padlock code would be 762663.)

Solution next week

#189 Going back in time

Solution

The time I first looked at the clock was 14:55:41.

The longest interval between palindromic times is 4 hours, 4 minutes and 11 seconds, which happens between 05:55:50 and 10:00:01, and then between 15:55:51 and 20:00:02. The shortest interval of 5 minutes and 10 seconds happens just before and after the hour, for example between 11:55:11 and 12:00:21.

Since my long gap was the second of the day, the time I first looked at the clock was 14:55:41, the next palindrome was at 15:00:51 and the long one began at 15:55:51.