Palindromes on a digital clock

Question

A palindrome is a number that reads the same forwards and backwards,such as $55$ and $12321$. How many times in a $24$-hour period of time on a digital clock does the number reveal a palindrome?

Answer 1

I have listed all possible times on a $24$-hour system that appear as palindromes on a digital clock. You may need to ignore the colon ($:$) in order to regard it a palindrome.

or example, $\text{2:52}$ is read backwards $\text{25:2}$, but ignoring the colon gives you the palindrome number $252$.

$$\begin{array}{|c|c|c|c|} \hline \text{0:00} & \text{0:10} & \text{0:20} & \text{0:30} & \text{0:40} & \text{0:50} \\ \hline \text{1:01} & \text{1:11} & \text{1:21} & \text{1:31} & \text{1:41} & \text{1:51} \\ \hline \text{2:02} & \text{2:12} & \text{2:22} & \text{2:32} & \text{2:42} & \text{2:52} \\ \hline \text{3:03} & \text{3:13} & \text{3:23} & \text{3:33} & \text{3:43} & \text{3:53} \\ \hline \text{4:04} & \text{4:14} & \text{4:24} & \text{4:34} & \text{4:44} & \text{4:54} \\ \hline \text{5:05} & \text{5:15} & \text{5:25} & \text{5:35} & \text{5:45} & \text{5:55} \\ \hline \text{6:06} & \text{6:16} & \text{6:26} & \text{6:36} & \text{6:46} & \text{6:56} \\ \hline \text{7:07} & \text{7:17} & \text{7:27} & \text{7:37} & \text{7:47} & \text{7:57} \\ \hline \text{8:08} & \text{8:18} & \text{8:28} & \text{8:38} & \text{8:48} & \text{8:58} \\ \hline \text{9:09} & \text{9:19} & \text{9:29} & \text{9:39} & \text{9:49} & \text{9:59} \\ \hline \text{10:01} & \text{11:11} & \text{12:21} & \text{13:31} & \text{14:41} & \text{15:51} \\ \hline \text{20:02} & \text{21:12} & \text{22:22} & \text{23:32} \\ \hline \end{array}$$ If, however, you are required to include the extra $0$ when appropriate, such as $\text{04:27}$ instead of $\text{4:27}$, then here are all possible combinations listed below. $$\begin{array}{|c|c|c|c|} \hline \text{00:00} & \text{01:10} & \text{02:20} & \text{03:30} & \text{04:40} & \text{05:50} \\ \hline \text{10:01} & \text{11:11} & \text{12:21} & \text{13:31} & \text{14:41} & \text{15:51} \\ \hline \text{20:02} & \text{21:12} & \text{22:22} & \text{23:32} \\ \hline \end{array}$$