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Black Box» Forums » General

Subject: Spoilers - game 80 has two valid solutions rss

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Wakefield Morys-Carter
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Oxford
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I've quite enjoyed playing Black Box this summer, both with one player hiding the atoms and with one or more players against the book. We discovered that for the final problem in the book (game 80 with five atoms) there is a second solution which is indistinguishable from the published one. The following photos show the two solutions -- all uncovered numbers are black "absorbed" pawns.

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Rich Charters
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Chandler
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Well found. The green takes quite a wild-ride in the 2nd solution, but it seems like there are two viable solutions.
 
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Chris Schumann
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It's one example of a more generic problem with the game: There are many ways to do this. Another example:


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The one on the inside is not detectable and could be in 1 of 4 positions.
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Wakefield Morys-Carter
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Yes, I saw someone mention that one on the Black Box + forum, though in that case the alternative solutions and the fact that they can't be distinguished are obvious.

I wonder if there are any cases when using four atoms. My hunch is that it's the added complexity of the fifth atom that allows for multiple solutions.
 
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