s u m o f t h e v a l u es in t h e t o p ro w : S = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 1 − 2 1 − 2 8 = 2 8 − 1 = 255 t h e s u m o f a ll t h e n u mb ers o n t h e c h ess b o a r d : S ⋅ 1 + S ⋅ 3 + S ⋅ 9 + S ⋅ 27 + S ⋅ 81 + S ⋅ 243 + S ⋅ 729 + S ⋅ 2187 = = S ⋅ ( 1 + 3 + 9 + 27 + 81 + 243 + 729 + 2187 ) = 255 ⋅ 1 − 3 1 − 3 8 = = 255 ⋅ − 2 − 6560 = 255 ⋅ 3280 = 836 , 400 A n s . t h e s u m o f a ll t h e n u mb ers o n t h e c h ess b o a r d i s 836 , 400
The sum of all the numbers on the chessboard is calculated to be 836400, by summing the products of the top row values (powers of 2) and left column values (powers of 3).
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