Starting from midnight, and assuming (a) it displays all four digits and (b) it displays in 24-hour format - there are 16 palindromic times...
0000 0110 0220 0330 0440 0550 1001 1111 1221 1331 1441 1551 2002 2112 2222 2332
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A 24 hour clock displays digits whose sum total equals the number of led's used to display them 94 times a day. A 12 hour clock displays them 108 times a day.
1
146
5 times
146