A father and son calculate that their current ages add up to 66. The father notes that his age is the exact reverse of his son's age (the same two digits in opposite order). Assuming the father is strictly older than the son, how many different valid age pairs could they be?
3 pairs
Representing the digits as 'a' and 'b', the sum is (10a + b) + (10b + a) = 11(a + b) = 66, so a + b = 6. With father > son, the digit pairs (a, b) can be (0, 6) [ages 6 & 60], (1, 5) [ages 15 & 51], and (2, 4) [ages 24 & 42]. This yields 3 valid pairs.
About this riddle
Math riddles hide a calculation inside a short story. Pull out the numbers, work out what is being asked, and watch for a trick such as a unit change.
Difficulty: Hard. More like this: Math riddles with answers or try Target 24 for a different kind of puzzle.
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