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There are 4 coins in a row and all are showing heads to start with. The coins can be flipped with the following rules
(a) The fourth coin from the left can be flipped any time
(b) An intermediate coin can be changed to tail only if its immediate neighbor on the right is heads and all other coins if any to its right are tails
(c) Only one coin can be flipped in one step
The minimum number of steps required to bring all coins to show tails is
Correct Answer: 8
One shortest sequence of states is $$HHHH\to HHTH\to HHTT\to THTT\to THHT\to TTHT\to TTHH\to TTTH\to TTTT$$. This uses exactly eight flips and satisfies the stated restriction at every step. Hence the minimum number of steps is $$8$$.
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