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 11 square, two 22, two 33, and of course the one 44.

Question

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 11 square, two 22, two 33, and of course the one 44.

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! :)

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11 answers
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Answer 1

MathMate answered
11 years ago

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.

Answer 2

HI answered
10 years ago

104

Answer 3

yea answered
9 years ago

The Grid looks like this:

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

Answer 4

哈羅 answered
9 years ago

what about ten by ten

Answer 5

DANZER answered
6 years ago

5368

Answer 6

HI thanks bro answered
5 years ago

thanks HI

Answer 7

fatty answered
5 years ago

afdfaf

Answer 8

Anonymous answered
3 years ago

Can someone say pls

Answer 9

Anonymous answered
2 years ago

4x4: 108

10x10: 5440

Answer 10

Anonymous answered
1 year ago

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

Answer 11

anonymous answered
1 year ago