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An 8 by 8 checkerboard has alternating black and white squares. How many distinct squares, with sides on the grid lines of the checkerboard (horizontal and vertical) and containing at least 4 black squares, can be drawn on the checkerboard?

Logic  Oct 12, 2018
 #1
avatar+3154 
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no 2x2 squares have 4 black squares

 

all 3x3 squares have at least 4 black squares, as do all 4x4, 5x5, 6x6, 7x7, and 8x8 squares.

 

there are 6x6=36 3x3 squares

there are 5x5=25 4x4 squares

there are 4x4=16 5x5 squares

there are 3x3=9  6x6 squares

there are 2x2=4  7x7 squares

there is   1          8x8 square

 

Summing we get 91 squares

Rom  Oct 12, 2018

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