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Discrete Mathematics Level 4

A pawn is placed on the lower left corner square of a standard \(8\) by \(8\) chessboard. A 'move' involves moving the pawn, where possible, either

  1. one square to the right,
  2. one square up, or
  3. diagonally one square up and to the right.

Using these legitimate moves the pawn is to be moved along a path from the lower left square to the upper right square.

How many such paths are there?

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Brian Charlesworth by Brian Charlesworth
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