### May 2006: Tait's 8 Coin Puzzle

In 1884 P. G. Tait presented the following puzzle (which he encountered while riding on a train). Start with

For example, here is a solution for six coins using four moves.

**eight**adjacent coins alternating heads and tails. By moving**four**pairs of neighboring coins (and without changing their order), rearrange the coins to obtain four tails followed by four heads with no gaps between any of the coins.For example, here is a solution for six coins using four moves.

Your solution should list the orders of the coins (including the gaps) at each stage.

May winners: Evan Templeton, Jon Rogers, Jared Lease, Gordon Clark, Shashwat AcharyaP.G. Tait, "Listing's *Topologie*,"* Philosophical Magazine*, January 1884

[See the solution to last month's puzzle, Queen Domination]