Problem 15 · 2025 Math Kangaroo
Hard
Number Theory
digit-sumcasework
Each card has two 3-digit numbers on it. Some of the digits are hidden (shown as ?). On one of the cards, the sum of the digits of the two numbers is the same. Which one?
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Answer: C — 982 and 1??
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Hint 1 of 2
For each card, find the digit sum of the fully shown number.
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Hint 2 of 2
Check whether the hidden number could ever reach that same digit sum.
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Approach: compare achievable digit sums
- 982 has digit sum 9 + 8 + 2 = 19.
- Its partner 1?? can reach a digit sum as high as 1 + 9 + 9 = 19 (the number 199).
- For every other card, the visible number’s digit sum is out of reach of its hidden partner.
- So the card with equal digit sums is ‘982 and 1??’.
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