Problem 6 · 2020 Math Kangaroo
Medium
Number Theory
cryptarithmplace-value
In the addition shown, different letters represent different digits and equal letters represent equal digits. The resulting sum is a four-digit number, with B different from zero. What is the sum of the digits of this number?
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Answer: B — BB
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Hint 1 of 2
Write A + AB + ABA as an expression in the digit values of A and B.
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Hint 2 of 2
Match it to the four-digit result BEBA and pin down each letter.
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Approach: convert the cryptarithm to place value and solve for the digits
- A + AB + ABA = 112A + 11B, and BEBA = 1010B + 100E + A.
- Setting them equal forces A = 9, B = 1, E = 0, so the sum is 1019.
- The sum of its digits is 1 + 0 + 1 + 9 = 11.
- Since BB = 11, the answer is BB.
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