Titles Question

[Angel Haroon]

Some square floors have been covered with white and grey tiles. Floors using 4 and 9 grey tiles are shown in the picture. Each floor has a grey tile in every corner and all the tiles around a grey tile are white. How many white tiles are needed altogether for a floor using 25 grey tiles?


I made a table like the one in the picture, but it took a lot of time is there an easy way to solve this.

 

[Steven G]

Can you show us your method and we can talk about improving it or get you to think about it in a different way?

 

[Angel Haroon]

Can you show us your method and we can talk about improving it or get you to think about it in a different way?

I tried this way too..
1 grey title is surrounded by 3 white titles
so
25 grey titles will have 3 x 25 = 75 white titles
which is wrong.

 

[Dr.Peterson]

I would take it in several steps.

Given a number of gray tiles, how can you find the total number of tiles in the first row?

Then, how many total tiles are needed, and how many are white?

The reason your thinking is wrong is that not every gray tile is surrounded by the same number of white, so they are not proportional.

 

[Steven G]

Note that to have a gray tile in the corner of the top row there must be an odd number of tiles in eachthat row. Same for the left column. So the size of the square must be odd x odd.

Now if this is an exam question and you have no idea how to do it then my note above will rule out 3 of the 5 choices.

Note that every other row is all white. This is a BIG hint.