Problem 10 · 2022 Math Kangaroo
Medium
Logic & Word Problems
careful-counting
Carl writes down a five-digit number. He then places a shape on each of the five digits (see picture). He places different shapes on different digits. He places the same shape on the same digits. Which number did Carl hide?
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Answer: A — 34426
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Hint 1 of 2
Same shape means same digit; different shapes mean different digits.
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Hint 2 of 2
The two diamonds sit in positions 2 and 3, so those digits must be equal.
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Approach: match equal shapes to equal digits
- The shapes are heart, diamond, diamond, club, spade - only positions 2 and 3 repeat.
- So digits 2 and 3 are equal and all the others are different from them and each other.
- Only 34426 has its 2nd and 3rd digits equal (4 and 4) with the rest distinct.
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