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The total of 100 white and black tiles will form a 10x10 square patter

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ohfred
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The total of 100 white and black tiles will form a 10x10 square patter [#permalink] New post   Updated on: 17 Oct 2023, 11:53
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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

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B

Originally posted by ohfred on 27 Dec 2010, 00:01.
Last edited by Bunuel on 17 Oct 2023, 11:53, edited 2 times in total.
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USCTrojan2006
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Re: The total of 100 white and black tiles will form a 10x10 square patter [#permalink] New post   27 Dec 2010, 00:14
ohfred wrote:
100 white and black tiles will be used to form a 10x10 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?

75
80
85
90
95


80?

90 white or black subtracted from 10 white or black.

At first I got 90, but realized the double counting I was doing.
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saurabhgoel
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Re: The total of 100 white and black tiles will form a 10x10 square patter [#permalink] New post   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
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Re: The total of 100 white and black tiles will form a 10x10 square patter [#permalink] New post   23 Jul 2014, 18:55
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ohfred wrote:
100 white and black tiles will be used to form a 10x10 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?

75
80
85
90
95


The attached illustration should help you understand how we arrived at the answer.

90-10 = 80

Answer is B
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Re: The total of 100 white and black tiles will form a 10x10 square patter [#permalink] New post   23 Jul 2014, 19:01
Answer = B

Please refer diagram below

90 - 10 = 80

Bunuel: Kindly change the "Topic Name" from "Re: Can someone explain this tile question?" to the question...

Thanks :)
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Re: The total of 100 white and black tiles will form a 10x10 square patter [#permalink] New post   17 Oct 2023, 11:53
Expert Reply
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


The least number of tiles of one color we can use is 10. If we place them on a diagonal of the square, both conditions are met.



The maximum difference in the number of tiles of each color is therefore, \(90 - 10 = 80\).


Answer: B
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Re: The total of 100 white and black tiles will form a 10x10 square patter [#permalink] New post   17 Oct 2023, 12:14
Take any color at minimum. Min =10
Remaining = 90

difference =80
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Re: The total of 100 white and black tiles will form a 10x10 square patter [#permalink]
17 Oct 2023, 12:14
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