Logan M
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Why is a single-corner twist not a valid position on a Rubik's cube?
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37 votes

Okay, I'll give a group-theoretic answer, since that was requested, which goes most of the way to a proof. I'm assuming you mean a 3x3x3 Rubik's cube. For larger cubes, the proof is just a little bit ...

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How many distinct unsolvable Rubik's cubes exist?
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25 votes

My answer at Why is a single-corner twist not a valid position on a Rubik's cube? basically explains this, but in simpler terminology here are the facts presented without proof. If you randomly ...

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Drawing lines on a map
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8 votes

I'll assume the cities lie on a flat plane, which seems to be the most reasonable interpretation of the question. Let's assume (for contradiction) that we had a city which is connected to at least 6 ...

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What is the smallest tic-tac-toe board to have a winning strategy?
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7 votes

6 or fewer cells will never make a board in which either player can force a win. On a 6 cell board, each player moves exactly thrice. To win, $X$ must pick 3 cells which happen to lie adjacent to ...

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