I am a two-digit number. If you multiply my digits together, the product equals my total value divided by 3. When you swap my digits, my value increases by 18. What number am I?
24
Let the number be 10a + b. Swapping the digits gives 10b + a = (10a + b) + 18, which simplifies to b - a = 2 (so b = a + 2). The product condition states a × b = (10a + b) / 3. Substituting b yields 3a(a + 2) = 11a + 2, which gives the quadratic 3a² - 5a - 2 = 0. Factoring gives (3a + 1)(a - 2) = 0, so a = 2 and b = 4. The number is 24.
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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