Six coins show heads H or tails T. The Starting Arrangement is H H H T T T and the Final Arrangement is T T T H H H, as illustrated. One step interchanges adjacent coins without flipping either coin. Find the minimum number of steps.
Each of the three H coins must cross each of the three T coins, requiring 3×3=9 reversals of H–T order. One adjacent interchange changes only one such crossing, so at least nine steps are needed. Moving each T left across all three H coins achieves exactly nine. **C**.
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