Problem 12 · 2020 Math Kangaroo
Stretch
Logic & Word Problems
sum-constraintwork-backward
Two thousand and twenty coins lie on a table, all showing heads. In each move you must turn over exactly three of the coins. What is the smallest number of moves needed so that every coin shows tails?
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Answer: C — 674
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Hint 1 of 2
Each coin must be flipped an odd number of times to end as tails.
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Hint 2 of 2
Three flips per move; how few moves cover 2020 odd-flip requirements?
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Approach: parity and a counting lower bound
- Each of the 2020 coins needs an odd number of flips, so at least 2020 coin-flips are needed.
- Each move makes 3 coin-flips, so at least 2020/3 rounded up = 674 moves.
- 674 moves give 2022 flips: flip 2019 coins once and one coin three times — all odd — which is achievable, so the answer is 674.
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