Christmas Streak 31/88: A Bit Farther

Tom is jumping around a \(4\times4\) 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 \(m,\) and the number of ways of doing so is \(r.\)

Find the value of \(mr.\)

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


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