a standard checkerboard with 8 blocks to a side contains 204 squares of various sizes. in how many such squares are there an equal number of red blocks and black blocks?
2 answers
im in a quick hurry please help
1by1 --- 64 of them
2by2 --- 49
3by3 --- 36
4by4 --- 25
5by5 --- 16
6by ----- 9
7by7 ---- 4
8by8 ---- 1
total = 204
There can only be an equal number of reds and blacks in the even-numbered squares, so
64 + 36 + 16 + 4 + 1 = 121
121 blocks have the same number of reds and blacks.
( e.g. a 3 by 3 square can have either
a) 4 reds and 5 blacks, or
b) 5 reds and 4 blacks. )
2by2 --- 49
3by3 --- 36
4by4 --- 25
5by5 --- 16
6by ----- 9
7by7 ---- 4
8by8 ---- 1
total = 204
There can only be an equal number of reds and blacks in the even-numbered squares, so
64 + 36 + 16 + 4 + 1 = 121
121 blocks have the same number of reds and blacks.
( e.g. a 3 by 3 square can have either
a) 4 reds and 5 blacks, or
b) 5 reds and 4 blacks. )
1 answer