Math problem with 4 square by 4 square grid?

Question

I have done this but I think I missed a step. The grid is 4 squares by 4 squares for a total of 16 square boxes in all. How many squares can you get out of the grid? I think its 30 but I am not the best at math. I drew a bunch of grids and tried it that way. But, here's the thing that's bugging me. I did this years ago and I think you can actually get squares using a section of 3 squares by 3 squares within the four square box

Oops! It cutoff. I hope all that makes sense.

Thanks everyone!

Answer 1

There are 16 (= 4*4) of the small squares.
There are 9 (=3*3) of the squares that take 4 small squares.
There are 4 (=2*2) of the squares that take 9 small squares.
There is 1 large square.

16 + 9 + 4 + 1 = 30, so you got it right.

I hope this helps!

Answer 2

Yes, it is 30 in all. There are 16 small squares, 9 2x2 squares, 4 3x3 squares and 1 4x4 square. 16 + 9 + 4 + 1 = 30.
These always can be solved by summing all the perfect squares up to the one you have. In other words, a 6x6 square has 36 + 25 + 16 + 9 + 4 + 1 total squares in it -- or 91 squares.

Answer 3

Draw it out on paper and then count then in terms of (1*1), (2*2), (3*3) and then the last one is the whole (4*4)
1 x 1 squares = 16
2 x 2 squares = 9
... Looking at your paper... Start in the bottom right and count the four that make that corner, then go up one and count again, then go up one last time and now you are counting the top "2x2" ... now move you initial starting point over by one square and count in 2x2 again, and go up by one each time, and then finally move your start over by one again and then go up again ... should have counted to 9 in the 2 x 2 squares
3 x 3 squares = 4
... looking at the paper count the same way as before
4 x 4 squares = 1
total squares = (16 +9 +4 +1) = 30.
Interesting point the numbers you found for each group (where 2x2 was a group and 1 x 1 was another group, they were all square numbers
16 = 4²
9 = 3²
4 = 2²
1 = 1²

Answer 4

4 Square Grid

Answer 5

Within a 4x4 square grid, you can draw a 1x1 box, a 2x2 box, a 3x3 box or a 4x4 box.

Number of 1x1 boxes = 16
Number of 2x2 boxes = 9
Number of 3x3 boxes = 4
Number of 4x4 boxes = 1

So total number of boxes = 16 + 9 + 4 + 1 = 30 :)

Answer 6

1 big one, 4 3*3, 9 2*2, and 16 of the smallest
1+4+9+16=30

You are quite right.

Answer 7

There is a formula for this problem.
For n square by n square grid, total number of squares is
1² + 2² + ... + n² or if you are familiar with sigma

n
∑(i)²
i=1

Answer 8

It's called a knight's tour. Yeah, look it up on wikipedia, they even have a friggin pictures showing the knight move and the trail it leaves It even gives different ways to do it, the history of it, etc. You spent all this time going to yahoo answers and didn't even google it first :p wikipedia would have been at the top.