Christmas Streak 31/88: A Bit Farther

Tom is jumping around a 4×44\times4 grid of circles with the following conditions:

  • He starts from any of the 16 circles.
  • He always jumps in a straight line from one circle to any other circle.
  • Each subsequent jump is farther than the last.
  • He doesn't visit a circle already visited.

The maximum number of circles that he can step on is m,m, and the number of ways of doing so is r.r.

Find the value of

Note: The grid is fixed on the ground, so a method obtained by rotating another is considered different.


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