Answers to Exercises
It isn’t that they can’t see the solution.
It is that they can’t see the problem.
— G. K. CHESTERTON, The Scandal of Father Brown (1935)
Mathematical Preliminaries Redux
1. (a) A beats B in 5 + 0 + 5 + 5 + 0 + 5 cases out of 36; B beats C in 4 + 2 + 4 + 4 + 2 + 4; C beats A in 2 + 2 + 2 + 6 + 2 + 6.
(b) The unique solution, without going to more than six spots per face, is
(c) A = {Fm−2 × 1, Fm−1 × 4}, B = {Fm × 3}, C = {Fm−1 × 2, Fm−2 × 5} makes 
; and we have Fm−2Fm+1 = Fm−1Fm − (−1)m. [Similarly, with n faces and , etc., ...
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