A digital clock shows the time as four digits in the 24-hour system, running from 00:00 through to 23:59. In one whole day, how many times does the display show four digits that are all the same?

Take the repeated digit d and test whether dd:dd is a legal reading. The hour part dd must be 23 or less, so d can only be 0, 1 or 2; the minute part dd must be 59 or less, which those three all pass. That gives 00:00, 11:11 and 22:22, so 3 times. The traps: 2 drops 00:00 from the list, forgetting that midnight is displayed as four zeros; 4 slips in 33:33, which no 24-hour clock ever reaches.