A digital clock displays hours and minutes in 24-hour format (00:00 to 23:59). At how many unique times during a single day is the sum of the digits in the hours equal to the sum of the digits in the minutes?
70
Let the hour digits be $H_1 H_2$ and minute digits be $M_1 M_2$. We need $H_1 + H_2 = M_1 + M_2$. The possible sums for hours range from 0 (00) to 1+9=10 (19). By systematically counting valid minute pairs for each possible hour sum, the total comes to exactly 70 matching times.
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Hard. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
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