John Conway posted the original insomniacs problem below, which assumes a 12 hour clock with no leading zeros. The following trickier problem also assumes a 12 digit clock. """ Here in washington state I am watching palindromic numbers go by in local time on my on my computers 12-hour clock without leading zeros. I count 281 seconds between two palindromes. How long will it be before I count 281 seconds between two number again? Regards Otto Original Problem:

There's a digital clock at my bedside that shows hours minutes and seconds, and which I usually look at the moment I wake up. A few days ago, I happened to wake up at a palindromic time, and out of interest, waited until the next palindromic time, and noticed the interval between them.

Last night exactly the same thing happened, but the interval was exactly four times as long as in the previous case. What did the clock read when I woke up last night?

John Conway