Question 550727: We call a time on a digital clock a palindrome if it is read the same way in either direction. For example, 5:45 is a palindrome. From noon to midnight, how many palindromes appear on a digital clock?
I'm not sure how to begin this, please offer me step by step explanation! Thanks :)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! 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
|
|
|
