H denotes a head-up coin and T a tail-up coin. Six coins begin HHHTTT and must become TTTHHH, as shown. A step swaps two adjacent coins without flipping either. Find the minimum steps.
Each of the three H coins must cross each of the three T coins. These nine H–T crossings each require an adjacent swap, giving a lower bound of nine. Moving each T left across all three H coins attains it. **9, C**.
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