There's still the question of optimality. Last I checked, Andy Latto proposed an argument that I found unconvincing. Were other people convinced? If so, could someone explain to me why you should never jump a frog over a frog or a toad over a toad? Jim Propp On Sunday, April 10, 2016, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
On 08/04/2016 16:24, Fred Lunnon wrote:
On Thursday, March 31, 2016, Gareth McCaughan <gareth.mccaughan@pobox.com>
wrote:
It's discussed very briefly in Winning Ways, which makes the assertion that from the standard initial position you just want to alternate between making as many penny moves as possible and making as many dime moves as possible but says nothing about other configurations or about proofs.
Are you sure this is the same puzzle? That strategy would result in T T - F F -> T - T F F -> - T T F F -> ?! which is plainly a cul-de-sac.
Well, unless I'm misunderstanding (WW is frequently rather terse) they say what I say they say, but of course you're right. I think what they actually mean is: make the obvious single move with one kind of piece, then switch to the other and *from then on* always move as many as possible. So:
T T - F F
single move with T:
T - T F F
as many F moves as possible:
T F T - F T F T F -
as many T moves as possible:
T F - F T - F T F T
as many F moves as possible:
F - T F T F F T - T
as many T moves as possible:
F F - T T
and I think this works in general. But it isn't what they actually say.
-- g
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