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Quarter rolling a die means triping it on any of the 4 sides adjacent to its base or face in contact with the flat surface. Using the assembled die and quarter chessboard:

  1. You can place and align the 1 x 1 die on any square of the board with its top face pips as initial count.

  2. By quarter rolling to any adjacent square once, you just add the top pips number of die on that square to previous count until all 16 square has pip numbers to be added.

How to get a maximum die roll (sum of all top face number of pips) by quarter rolling a standard die on every square of a 4 x 4 checkerboard?

  • $\begingroup$ Is it allowed to pass on a square twice? If so do you consider the first number of the last? $\endgroup$
    – Florian F
    Commented Jul 26, 2020 at 11:16
  • $\begingroup$ @Froilan -it is only allowed to role on any square once. You can find many possible ways (mirror or symmetric) to pass all 16 square starting on - corner , side & middle square. $\endgroup$
    – TSLF
    Commented Jul 27, 2020 at 18:19

1 Answer 1


Early result:

Starting anywhere in this grid, with the die in the appropriate orientation, follow the path for a sum total of 70 pips.
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I started with 6-5-4-6 from various positions. This is the highest total I have achieved. Should have bonus points for being a closed Hamiltonian circuit.

  • $\begingroup$ Was this answer accepted because it is optimal? If so, how can you prove it? $\endgroup$
    – melfnt
    Commented Jul 27, 2020 at 8:21
  • $\begingroup$ @melfnt An exhaustive search using computer programming proves this to be optimal. $\endgroup$ Commented Jul 27, 2020 at 17:44

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