Скачать или смотреть A father and son's ages are digit-reverses and add up to 66—what are the possible age pairs?

Here’s a neat little age puzzle that mixes arithmetic with a dash of pattern-spotting. The puzzle: the sum of a father’s and son’s ages is 66, and the father’s age is the son’s age written backwards (for example, 51 and 15). Your job is to find every pair of whole-number ages that satisfy both conditions.

Quick method: call the father’s age a two-digit number AB (which means 10·A + B) and the son’s age BA (10·B + A). Their sum is (10A + B) + (10B + A) = 11(A + B) = 66. So A + B must be 6 (because 66 ÷ 11 = 6). Now list nonnegative integer digit pairs (A,B) where A and B are digits 0–9, A ≠ 0 for the father’s two-digit age, and A + B = 6. That gives: (1,5), (2,4), (3,3), (4,2), (5,1), (6,0). Convert those to ages (father, son): (15,51) would be reversed and invalid because father must be older — so reject pairs where the “father” would be less than the son. Valid two-digit father ages from our allowed A values are 51, 42, 33, 24, 15, 60 — but father must be older than the son, so valid realistic pairs (father, son) are (51, 15), (42, 24), and (60, 06). Note that (33,33) is symmetric and also sums to 66, but digits reversed give the same age; whether you accept this depends on whether “reversed” allows identical digits — strictly, it does, but it’s not a father/son realistic pair. The classic accepted answers: (51,15), (42,24), (60,06).

#puzzle #riddle #ageriddle #brainteaser #mathriddle #logicpuzzle #numbers #mindgames #lateralthinking #fun #quiz #challenge #brainteasers #puzzlelover #teachermaterials #education #mathfun #family #fatherandson #digits #digitreversal #algebra #quickmath #puzzletime #thinking #mentalgym #clever #problem-solving #intellectual #trivia #Sapionova