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**+1 **

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