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knight riddle
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Reed Nelson committed Nov 6, 2023
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- [Magic Square](#magic-square)
- [Mutilated Chessboard Problem](#mutilated-chessboard-problem)
- [Mutilated Cube Problem](#mutilated-cube-problem)
- [Some Knights](#some-knights)
- [Two Ropes](#two-ropes)
- [Hard Boiled](#hard-boiled)
- [The Great Divide](#the-great-divide)
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The minimum number of cuts is 6. Proof: Consider the middle cube. There is no way to reveal any two of its faces in a single cut. And then it is trivial to see that it can indeed be done in 6 cuts.
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## Some Knights

How many knights can you place on a chessboard such that none of them can attack another?

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<summary>Solution</summary>
A knight's movement pattern necessitates that it lands on a square of the opposite color from the one it starts on. So the optimal placement would be 32 knights, one for each black (white) square on the board.
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## Two Ropes

You have two ropes, each of which will burn at varying speeds throughout their lengths, but by the end have burned for exactly 1 hour. How can you measure 45 minutes?
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