Crack the briefcase code from four clues

Question

A locked briefcase opens with a three-digit code (a hundreds digit, a tens digit, and a units digit). A note left by the owner lists four facts about it: - The three digits add up to 15. - The whole number is odd. - The hundreds digit is exactly twice the tens digit. - The units digit is smaller than the hundreds digit. What is the code?

Accepted Answer

Call the digits h (hundreds), t (tens), u (units). Start with the strongest clue: h = 2t. Since h is a real hundreds digit it runs from 1 to 9, so t can only be 1, 2, 3, or 4 (any bigger and h would exceed 9). Now use the sum h + t + u = 15. Because h = 2t, this becomes 2t + t + u = 15, i.e. u = 15 - 3t. Test each allowed t: - t = 1 \Rightarrow u = 12, impossible (a digit can't exceed 9). - t = 2 \Rightarrow h = 4,\ u = 9, gives 429. - t = 3 \Rightarrow h = 6,\ u = 6, but u = 6 is even, and the number must be odd (its units digit must be odd). Reject. - t = 4 \Rightarrow h = 8,\ u = 3, gives …

Crack the briefcase code from four clues

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