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avatar+1304 

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 $16$ yellow tiles, how many gray tiles are there?

 Dec 19, 2023
 #1
avatar+828 
+1

 

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 $16$ yellow tiles, how many gray tiles are there?  

 

Think of these criteria:  "The corners are yellow, the center is yellow"   

 

That accounts for 5 yellow tiles.  It leaves 11 yellow tiles for "all the tiles along the diagonal in between"  

 

The number of tiles along each diagonal in between will be the same, so it must be divisible by four.  

 

11 is not evenly divisible by 4, so I believe there's something wrong with the problem as stated.  

.

 Dec 19, 2023
 #2
avatar+129197 
+1

Agree with Bosco

 

Call the total number of  yellow tiles  (not counting  the one in the  center) = 4n

 

Adding the one  in the  center the  total number of yellow tiles = 4n + 1

 

But this  number is odd  so it can't  = 16

 

 

cool cool cool

 Dec 20, 2023

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