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.
Floor tile problem
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linear-algebra
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1If you found this online it is always good to provide the link of the source. Also you should tell us what you did. – 2012-06-14
1 Answers
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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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0@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. – 2012-06-14