Problem 3 · 2022 Math Kangaroo
Easy
Logic & Word Problems
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One of the five coins A, B, C, D or E should be moved to an empty square so that each row and each column ends up with exactly two coins. Which coin should be moved?
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Answer: C — C
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Hint 1 of 2
Count how many coins are in each row and in each column right now.
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Hint 2 of 2
Find the one row that has too many and the one column that has too many; the coin sitting where they cross is the one to move.
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Approach: balance rows and columns
- Counting coins, one row has three coins (too many) and one row has only one (too few).
- Likewise one column has three coins and another has only one.
- The coin that sits in BOTH the overloaded row and the overloaded column is the one to move.
- That coin is C; moving it to the empty cell of the short row and short column fixes every count to two.
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