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The foor of a rectangular room is covered with equal numbers of red and blue square tiles. The room is x tiles wide and y tiles long. If only red tiles are placed around the edge of the room and all of them are used for the boundary, nd all possible values of x and y.

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You should not pose your questions in imperative form. If this is homework tag it so and show your work. –  Listing Jun 14 '12 at 16:40
    
i apologise found this online, want to see if what i did was correct –  fosho Jun 14 '12 at 16:42
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If you found this online it is always good to provide the link of the source. Also you should tell us what you did. –  Listing Jun 14 '12 at 16:43

1 Answer 1

Hint: given $x$ and $y$, can you make expressions for the number of border tiles and the number of non-border tiles? It often helps to draw a picture-it is easy to get the corners wrong.

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2(x-2)+2y = (x-2)(y-2) –  fosho Jun 14 '12 at 17:59
    
would that be correct? –  fosho Jun 14 '12 at 17:59
    
@Daniel: That is right. Expanding, we have $xy-4(x+y)+4=0$ If $x=y$, this becomes $x^2-8x+4=0$ which has no solutions. We can then assume $x \gt y$ and solve for $x$, getting $x=\frac {4y-4}{y-4}$ and look for values of $y$ which give an integral result. –  Ross Millikan Jun 14 '12 at 18:10
    
thanks! just checking! –  fosho Jun 14 '12 at 18:11

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