Question 1

Sixteen coins are arranged in a row on a table such as first coin has its head side up the second- tail and it continues in this alternate pattern till the last coin. In a single move you are permitted to select an arbitrary sequence of adjacent coins and to replace each head facing coin to tail and each tail facing coin to head.
Determine the minimum number of moves such that all 16 coins are tail side up.

Comments on Question 1

Solution

Many possible solutions are there but the no of moves cannot be less than 8 example of one such solution:
Turn middlemost tail up into head up, then 3 heads into tails, then 5……so on following the pattern 8 moves.
If we say let S be the count of no. of adjacent coins different from each other. Then no matter what move we take in a single move S will reduce only to S-2 which means we need min 8 moves to reduce it to zero.