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Solution to Nack's retro puzzle

Posted By: Timothy Chow
Date: Sunday, 4 May 2014, at 11:30 p.m.

In Response To: Puzzle, part deux -- still dedicated to Timothy Chow (Nack Ballard)

I finally got back to Nack's puzzle today, and solved it. Let me mention that prior to my "interim report," I spent a fair amount of time on a wild goose chase, thinking that since Nack didn't say which player was on roll, perhaps Blue actually started the game. I now believe that that's impossible (though I didn't actually prove it), but one can come surprisingly close.

Anyway, the solution I came up with was:

W: 13/7(4)
B: 13/7(4)
W: 13/10 8/2
B: 24/8
W: 6/4(2) 6/2
B: 7/5(2) 6/4(2)
W: 8/5(2) 6/3(2)
B: 24/4
W: 24/23(2) 7/6(2)

I'll leave the nactation for others to figure out. :-)

The solution is not unique, because both players have some freedom choosing the order in which to play their moves. However, there are some constraints. White has to clear her midpoint before Blue can play 24/8; Blue has to play 24/8 before White makes her 5pt with 8/5(2) 6/3(2); Blue has to wait for White to clear her 6pt with 8/5(2) 6/3(2) before he can play 24/4; and White has to wait for Blue to play 24/4 before she can play 24/23(2) 7/6(2).

I don't know whether there are other solutions that are not just transpositions of the above solution. I spent enough time on the problem that I suspect that there aren't, but again I didn't prove anything.

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