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My square patio is tiled with square tiles, all the same size.  All the tiles are gray, except the tiles along the two diagonals, which are all yellow.  (The corners are yellow, the center is yellow, and all the tiles along the diagonal in between are yellow.)  If there are $20$ yellow tiles, how many gray tiles are there?

 May 23, 2024
 #1
avatar+129514 
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Can't be done with 20 yellow tiles

 

The center tile is  yellow.....this leaves 19 yellow tiles that must be distributed symmetrically along each diagonal....but this means that each half-diagonal would have to contain 19/4 tiles....but 19/4  isn't an integer

 

cool cool cool

 May 23, 2024

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