Game of the Week, 2/3/2001

Please imagine the following lines sung in a Broadway/operatic voice to a haunting tune:

It is the old re-
It is the old re-

Our game is soli-
Our game is soli-

My wife and I went to the art cinema last night and took in Dancer in the Dark. At first I perceived the movie to be so sad that I just did not want to be there. I tried not to watch, or listen. Often I can do that trick at that particular theater. When the movies are in foreign tongues - ignoramus that I am - I can simply close my eyes and drift off to sleep. But this movie is set in the USA and is in English, though the heroine is a Czechoslovakian immigrant, and that trick did not work at all.

Then my angst-ridden mind found, suddenly, a peaceful little island. It occurred to me, "Hey! I still don't have that game of the week!" I closed my eyes again, and started to visualize some moves. 8+ 1(9)2 1(10)1[2,3] Just like last week. I remembered that last week Left now played 4(11)10. (This morning I am thinking that I probably made a horrible blunder in my annotation of that game, but I am not going to pursue that line of thought today.) I also remembered that the alternative 4(11)5 looked very plausible. The sphere S(2) will produce two survivors, unless spot # 10 plays outwards, and it is reasonable for Left to attempt to dry up the sphere S(4) and attempt to limit it to three survivors, for a winning total of five survivors. 4(11)5 If Left wants to dry up the sphere S(4), then it certainly makes sense for Right to go for fecundity. (It makes sense, at least, in solitaire play. Real play between two keen adversaries will undoubtedly hold many surprises. (Folks, we need to get this ball rolling.)) 4(12)4[6,7] Stop me if I am being repetitive, but often it seems that the player needing fecundity can usefully resort to UT creation. Now at this point Left has all sorts of tries. I found the position thoroughly bewildering, especially blindfold. I'm not good at that sort of thing. My guru, by the way, the obscure but amazing chess master Charles Walter, can play blindfold chess effortlessly, but he has no interest in sprouts. 6(13)12 I came up with this move, which turned out to be, in the words of Bobby Fischer, a "lemon". Much later that night - back home - I used paper and pencil and looked at several other tries. I suspect Right is winning, but this position needs much more exploration. Here are some lines: (A) 5(13)12 2(14)10 Right wins. I will explain in a minute. (B) 10(13)11 12(14)13 I think Right wins. The spheres S(2) and S(5) are both switches and I think they are both comparable in terms of waiting moves (Sprague-Grundy numbers). If so, Right will be able to force Left to move first to the trap S(6). (C) 5(13)10 11(14)12 Again, I think the switches S(2) and S(5) are exactly comparable in terms of waiting moves. (D)5(13)5 11(14)12[13] Easy one. The sphere S(2,14) has six cannibals and will produce four survivors. Right wins the cannibal war. 9(14)10[2] Dancing in the dark, I found this move just in time to begin to be ravished by that gorgeous, insane film. The sphere S(5,6) is a trap, because of symmetry. Right wins the cannibal war. A similar symmetrical trap appears in line A above. It has occurred to me this morning that I should call such a trap a Gardner trap, in honor of Martin Gardner who popularized sprouts in a memorable "Mathematical Games" column, and who pointed out the symmetrical theme (if memory serves) in that column.

It was after midnight when we returned to real life. I said, "I always did like musicals." My wife looked as if she were about to cry. As we walked along the margins of the most wonderful place in the world, the campus of the University of South Carolina, I remembered our cat Yangi, and suddenly I burst into song with my still fine baritone voice:

Where are my pa-rents?
When will they e-ver

And my beautiful Korean wife replied, her strong, crystal voice echoing musically through the night,

For I am wai-ting.
And I am on the

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