+0  
 
0
146
2
avatar

My 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 $89$ yellow tiles, how many gray tiles are there?

 Apr 19, 2020
 #1
avatar+69 
0

We can start by removing the center tile, because all four diagonals over lap on that tile. We'll add it back later. 88/4=22. which means there are 22 tiles per half, 44+1(the center tile) total tiles per side, which means there are a total of 1936 tiles. Subtracting 89, we get 1847

 Apr 20, 2020
 #2
avatar+69 
+1

For all the AOPS students here, the solution is 1936. I turned it in and it said it was correct so have fun cheating!

 Apr 24, 2020

29 Online Users

avatar
avatar
avatar
avatar