Visualize a 4x4 grid of unit squares, evenly arranged. Each unit square symbolizes a number that represents its involvement in forming larger squares within the grid, ranging from 1x1 to 4x4 squares. The top row central numbers are shown as '6', which indicates that these unit squares are included in one 1x1 square, two 2x2 squares, two 3x3 squares, and one 4x4 square. The pattern of such numbering spreads across the entirety of the 4x4 grid. This mathematical concept evokes curiosity in understanding the fundamental pattern and the algebraic logic behind it.

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! :)

104

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.

The Grid looks like this:

4 6 6 4
6 10 10 6
6 10 10 6
4 6 6 4

5368

thanks HI

what about ten by ten

I'm confused, what is the 10x10 answer???

The 10x10 answer is 5368

Can someone say pls

4x4: 108

10x10: 5440