Puzzle of the Week #161 - Coin Flipping part 2


Following on from last week’s coin flipping puzzle, where a horizontal or vertical line of three coins could be flipped together, with the object being to end with all the coins heads up. I’ll introduce a new move now – a diagonal (45 degree) line of three coins can also be flipped together. It turns out that with this new rule, as long as the arrangement of coins is big enough, any initial arrangement can be solved. But the question is: how big is big enough?

Find the arrangement with the fewest coins, such that any starting arrangement of heads or tails can be made all heads by a series of three-in-a-row flips in horizontal, vertical or diagonal directions.

(The coins must lie in a rectangular grid pattern. If there are spaces in the grid without coins, then a triplet of coins you wish to flip cannot bridge across the gaps).