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I have some square tiles.

Thu Jan 17, 2013 10:54 pm  by tartle

I have some square tiles. Half of them are black and the other ones are white. I arrange them so that the black ones form a rectangle and the white ones make a border around them one tile thick. I have no tiles left over. How many tiles do I have?
Mon Mar 04, 2013 10:44 pm  by Allstar

[b]spoiler alert[/b]
48, 24 black and 24 white. The black rectangle is 4x6.[/b]
Fri Jul 15, 2016 5:39 am  by Dzallen

There are only 2 solutions: 48 tiles with 4*6 black rectangle, or 60 tiles with 3*10 black rectangle

The difference in tiles between the white tiles and the outer most layer of the black rectangle is 8 tiles (2 tiles for each side). Therefore the inner black rectangle must have 8 tiles, which can be arranged as 2*4 or 1*8, giving the whole black rectangle as 4*6 or 3*10.
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