Problem 20 · 2024 Math Kangaroo
Stretch
Algebra & Patterns
cryptarithmplace-value
Cards with the same shape hide the same digit, and cards with different shapes hide different digits. Kim lays out the cards so that both calculations shown on the right are correct. What number does Kim get for triangle × circle × square?
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Answer: D — 28
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Hint 1 of 3
Each shape stands for one digit, and the two-shape answers on the right are two-digit numbers.
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Hint 2 of 3
When you add two single digits, the answer is at most 9 + 9 = 18, so its tens digit can only be 1.
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Hint 3 of 3
That tells you what the square is; then try a few values for the triangle until both pictures come out right.
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Approach: the tens digit of a sum of two single digits must be 1, then check triangle values
- Triangle + triangle is a two-digit number, but adding two single digits can give at most 18, so its tens digit is 1: the square is 1.
- The second picture says circle + triangle = the two-digit number 'square square' = 11.
- Try triangle = 7: then 7 + 7 = 14, so the answer is 1 then 4, meaning circle = 4; and circle + triangle = 4 + 7 = 11. Both pictures work!
- So triangle × circle × square = 7 × 4 × 1 = 28 (D).
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