A logic problem by A Former Brilliant Member

Logic Level 2

As shown, three 3-digit numbers have a 4-digit sum. Different letters represent different digits. What is the greatest prime factor of the sum, A C C A ‾ \overline{ACCA} .


The answer is 37.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Marta Reece
Dec 14, 2017

Last column (units place): B + B + A = 10 + A = > B = 5 B+B+A=10+A=>B=5

Middle column (tens place): B + B + A + 1 = 10 + C = > C = A + 1 B+B+A+1=10+C=>C=A+1

First column (hundreds place): B + B + A + 1 = 10 × A + C = 10 × A + A + 1 = > 10 × A = 10 = > A = 1 B+B+A+1=10\times A+C=10\times A+A+1=>10\times A=10=>A=1

C = A + 1 = 2 C=A+1=2

A C C A = 1221 = 3 × 11 × 37 ACCA=1221=3\times11\times\boxed{37}

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