Question 550727
At 12 o' clock, there is only one way to get a palindrome and it's at 12:21


-------------------------------------------------------

At 1 o' clock, there are 6 ways to have a palindrome and they are



1:01, 1:11, 1:21, 1:31, 1:41, 1:51



At 2 o' clock, there are 6 ways to have a palindrome and they are


2:01, 2:11, 2:21, 2:31, 2:41, 2:51


etc... all the way up to 10 o' clock (but not including 10 o' clock)


There are 6 palindromes for each hour in the list above and there are 9 hours from 1 o clock to 9 o clock. So there are 6*9 = 54 palindromes from 1 to 9 o clock


-------------------------------------------------------

From 10 o' clock on to midnight, there are only 2 ways to get a palindrome and they are:


10:01, 11:11



So there are 1+54+2 = 57 palindromes total