Problem 8 · 2024 Math Kangaroo
Medium
Logic & Word Problems
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There are 6 coins on a table, each with heads facing upwards. On each move we turn over exactly 4 of the coins. What is the minimum number of moves we must make so that all coins are left with heads facing downwards?
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Answer: B — 3
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Hint 1 of 2
Every coin must end face-down, so each must be flipped an odd number of times in total.
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Hint 2 of 2
Six odd flip-counts add to an even number equal to 4 × (moves); find the smallest move count that finishes the job.
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Approach: track flip parities and test small move counts
- To go from heads to tails, each of the 6 coins must be flipped an odd number of times.
- One move changes only 4 coins; two moves cannot make all six counts odd.
- Three moves can: choose the four-coin sets so every coin is flipped an odd number of times.
- The minimum is 3 moves.
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