# Posts Tagged: 15-puzzle

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## censured post : bloggers’ block

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Below an up-till-now hidden post, written november last year, trying to explain the long blog-silence at neverendingbooks during october-november 2007… A couple of months ago a publisher approached me, out of the blue, to consider writing a book about mathematics for the general audience (in Dutch (?!)). Okay, I brought this on myself hinting at… Read more »

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## The Mathieu groupoid (1)

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Conway’s puzzle M(13) is a variation on the 15-puzzle played with the 13 points in the projective plane $\mathbb{P}^2(\mathbb{F}_3)$. The desired position is given on the left where all the counters are placed at at the points having that label (the point corresponding to the hole in the drawing has label 0). A typical… Read more »

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## The 15-puzzle groupoid (2)

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In the 15-puzzle groupoid 1 we have seen that the legal positions of the classical 15-puzzle are the objects of a category in which every morphism is an isomorphism (a groupoid ). Today, we will show that there are exactly 10461394944000 objects (legal positions) in this groupoid. The crucial fact is that positions with the… Read more »

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## The 15-puzzle groupoid (1)

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Before we go deeper into Conway’s M(13) puzzle, let us consider a more commonly known sliding puzzle: the 15-puzzle. A heated discussion went on a couple of years ago at sci-physics-research, starting with this message. Lubos Motl argued that group-theory is sufficient to analyze the problem and that there is no reason to resort to… Read more »

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## Conway’s puzzle M(13)

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In the series “Mathieu games” we describe some mathematical games and puzzles connected to simple groups. We will encounter Conway’s M(13)-puzzle, the classic Loyd’s 15-puzzle and mathematical blackjack based on Mathieu’s sporadic simple group M(12).