MATH
posted by mathemagiacian on .
A four by four grid of unit squares contains squares of various sizes (1 by 1 through 4 by 4), each of which are formed entirely from squares in the grid. In each of the 16 unit squares, write the number of squares that contain it. For instance, the middle numbers in the top row are 6s because they are each contained in one 1*1 square, two 2*2, two 3*3, and of course the one 4*4.
What is the sum of all sixteen numbers written in this grid?
How about a ten by ten grid?
I really hope to see the answer. Thanks! :)

What did you get?
You would be well to do the 4x4.
If you have difficulties, start with a 1 by 1, then 2 by 2 and then 3 by 3 grid. You will find a pattern that you can use later.
Once done, do an n × n grid and check if the answer for n × n works for n=4. 
104

The Grid looks like this:
4 6 6 4
6 10 10 6
6 10 10 6
4 6 6 4 
what about ten by ten