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Problem of the Day #286: 3D Slider Puzzle December 30, 2011

Posted by Saketh in : potd , trackback

Sid has decided to take the classic “slider puzzle,” pictured below, to the third dimension.

He divides a $3$x$3$x$3$ frame into $27$ $1$x$1$x$1$ cells, $26$ of which contain a unit cube. These cubes are labeled from $1$ to $26$. Given any initial configuration, the goal is to slide the cubes around so that cube $n$ and cube $27-n$ swap positions. For how many distinct initial configurations is this possible?

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