Here is a table of the results:--

a b c Ways.

A = 8 + 17 + 21 = 46

B = 0 + 17 + 21 = 38

C = 15 + 31 + 39 = 85

D = 17 + 29 + 39 = 85

E = 1 + 0 + 0 = 1

-- -- -- ---

41 94 120 255

I have not attempted the task of enumerating the ways of dividing a

board 8 × 8--that is, an ordinary chessboard. Whatever the method

adopted, the solution would entail considerable labour.

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