Escape RoomRiddle #1401
A brass plate on the lockbox says: 'My three-digit code is exactly twelve times the sum of its own digits.' What's the code?
Hint: The code is small. Start in the 100s.
Answer
108
100a + 10b + c = 12a + 12b + 12c gives 88a = 2b + 11c. With single digits, a must be 1, so 2b + 11c = 88, which only works with c = 8 and b = 0. Check: 1 + 0 + 8 = 9, and 12 times 9 is 108.
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