Problem 21 · 2025 Math Kangaroo
Stretch
Number Theory
digit-sumsubstitution
In the six-digit number PAPAYA, different letters stand for different digits and equal letters stand for equal digits. It is also given that Y = P + P = A + A + A. What is the value of P × A × P × A × Y × A?
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Answer: A — 432
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Hint 1 of 2
The clues say Y = 2P and Y = 3A — so 2P = 3A with single digits.
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Hint 2 of 2
Find digits where twice P equals three times A, then read off Y.
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Approach: solve the digit equations, then multiply
- Y = P + P = 2P and Y = A + A + A = 3A, so 2P = 3A.
- The simplest distinct digits are A = 2, P = 3, giving Y = 6.
- Then \(P\times A\times P\times A\times Y\times A = 3\cdot2\cdot3\cdot2\cdot6\cdot2 = 432\), which is (A).
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