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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 5 yellow tiles, how many gray tiles are there?

 Jun 25, 2023
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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 5 yellow tiles, how many gray tiles are there?   

 

Here's the key info:   

                                   The corners are yellow...  

                                    the center is yellow...  

                                    there are 5 yellow tiles...  

 

There are four corners and one center.  

That's five yellow tiles right there.  

That's all of them.  There are no more yellow tiles.  

 

So the patio has to be a 3 x 3 square.  Draw it if you doubt me.  

The 3 x 3 patio has nine tiles in total.  

Five tiles are yellow, therefore the other four tiles are gray.  

.

 Jun 29, 2023

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