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Solution to how many moves on average it take a randomly moving knight to return to the starting square

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A solution to a randomly moving Knight via monte carlo simulation

The estimate mean number of moves from 10 000 simulations is 114, note that on other seeds, this value ranges between 111 - 116, performing more simulations should mean the value converges to 112.

knight.jpg

The theoretical solution is

  • Dark blue: 42
  • Medium blue: 56
  • Light blue: 84
  • Yellow: 112
  • Red: 168

theoretical.jpg

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Solution to how many moves on average it take a randomly moving knight to return to the starting square

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