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Difficulty:
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The total of 100 white and black tiles will form a 10x10 square pattern. Each row must contain at least one black tile, and each column must contain at least one white tile. What is the maximum possible difference between the number of black and white tiles used?
A. 75
B. 80
C. 85
D. 90
E. 95
M14-20
A. 75
B. 80
C. 85
D. 90
E. 95
M14-20
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USCTrojan2006
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27 Dec 2010, 00:14
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ohfred
80?
90 white or black subtracted from 10 white or black.
At first I got 90, but realized the double counting I was doing.
27 Dec 2010, 00:53
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You required 100 tiles in total
As per question we have to find maximum difference possible between white and black tiles.
So, we have to find, as per condition, maximum white tiles(black) can be used and minimum blac tiles(white) tiles that must be used.
In any case, maxium black and white tiles that can be used to form the square is 90.( 9 tiles of same color in any row or column:: 9 * 10).
and minimum blac or white tiles that can be used to form the squaare is 10( 1 tiles every row or column = 1 * 10 )
90 - 10 = 80
As per question we have to find maximum difference possible between white and black tiles.
So, we have to find, as per condition, maximum white tiles(black) can be used and minimum blac tiles(white) tiles that must be used.
In any case, maxium black and white tiles that can be used to form the square is 90.( 9 tiles of same color in any row or column:: 9 * 10).
and minimum blac or white tiles that can be used to form the squaare is 10( 1 tiles every row or column = 1 * 10 )
90 - 10 = 80
