Re: Coin puzzle (spoiler)

[Jeff Weisberg <jaw+phlpm@tcp4me.com>]

| Maybe I'm missing something, but I don't see how this helps since the
| coin pattern can be rotated while you're making your moves...

well, the important bits in solving it are:
	- there are only 3 unique, non-winning arraignments of coins
		HTHT, HHTT, HHHT
	- there are only 3 possible, non-null moves
		flip one (N)
		flip 2 next to each other (N+E)
		flip 2 across from each other (N+S)
	- certain combinations of moves do interesting things
	  independent of any rotation:

		HTHT + N+S always yields a win,
		HHTT + N+S always yields another HHTT => is a no-op
		HHHT + N+S always yields another HHHT => is a no-op

		HHTT + N+E always yields a win or an HTHT
		HHHT + N+E always yields another HHHT => is a no-op

		HHHT + N always yields a win, HTHT or HHTT

given the sequence: NS, NE, NS, N, and the 3 possible configs:

	HTHT + NS => always a win
	HHTT + NS => no change
		+ NE => win or HTHT
		  + NS => always a win

	HHHT + NS => no change
		+ NE => no change
		  + NS => no change
		    + N => either HTHT or HHTT - so repeat the sequence


	--jeff

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