A tangled age riddle that nests four different moments in time
Mary and Ann's combined ages are 44. Mary is twice as old as Ann was when Mary was half as old as Ann will be when Ann is three times as old as Mary was when Mary was three times as old as Ann. How old is Mary?
Reveal the answer
Mary is 27 1/2 and Ann is 16 1/2. Untangling it means turning each nested clause into its own algebraic statement and solving them as one system; it resolves exactly, fractions included. Sam Loyd devised the puzzle, and Henry Dudeney reprinted it as 'How Old Was Mary?' in Amusements in Mathematics (1917).