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number grids...very stuck!!! watch

1. hiya ne1 i need to find out the formula for squares on a 15 x 15 number grid

my results r as follows
2 x 2 = diff 15
3 x 3 = diff 60
4 x 4 = diff 135
6 x 6 = diff 365
7 x 7 = diff 540

2. (Original post by xxclairexx100)
hiya ne1 i need to find out the formula for squares on a 15 x 15 number grid

my results r as follows
2 x 2 = diff 15
3 x 3 = diff 60
4 x 4 = diff 135
6 x 6 = diff 365
7 x 7 = diff 540

You'll have to give a bit more information than that I'm afraid. Could you explain what the "diff" is please?
3. well...
i have to take a 15 x 15 grid and pick 2 x 2 squares for example
1 2
16 17 ..then i have to times the top rightby the bottom left
1 x 17 = 17
2 x 16 = 32 .... the difference between the 2 is 15
once i have doen that i had to do the same but with 3 x 3 boxes and so on....there is a formula that will help me with out drawing it all out but i cant work it out
4. I vaguely know what she means... when you put a 2x2 'square' around four numbers in a number grid, the difference between two of the numbers is 15... something like that. Oops, never mind, she already explained...

xxclairexx100, since you have already posted this problem before and someone just gave you the answer, how about you work it out this time? All of those results are divisible by 15 (coincidentally... or maybe not... the size of your grid)... tell me what you get from there.
5. well yer there gonna b if its on a 15 by 15 grid but that doesnt five you a formula
6. I was hinting for you to divide by 15 and tell me what you got.
7. divide wot by 15 i have no idea wot ur on about
8. (Original post by xxclairexx100)
well...
i have to take a 15 x 15 grid and pick 2 x 2 squares for example
1 2
16 17 ..then i have to times the top rightby the bottom left
1 x 17 = 17
2 x 16 = 32 .... the difference between the 2 is 15
once i have doen that i had to do the same but with 3 x 3 boxes and so on....there is a formula that will help me with out drawing it all out but i cant work it out
well let bottom right be n and so u have n * n+16 and also (n+1) * (n+15)

so diff is (n+1)(n+15)-n(n+16)=n^2-n^2+16n-16n+15

when expanding u can c that everything cancels except for the 15
9. forget it i just dunt get it im gnna fail
10. Are you doing GCSE maths as some sort of joke? Come on, please read what I'm saying and try to understand it.

You've told me that for an NxN square on a 15x15 grid, your results are:
N=2 Difference=15
N=3 Difference=60
N=4 Difference=135
N=5 Difference=365
N=6 Difference=540

All your differences are divisible by 15. Divide them by 15 and tell me what you get.
11. when i dived them by 15 i get
2x2 = 15 = 15/15 = 1
3x3 = 60 = 60/15 = 4
4x4 = 135 = 135/15 = 9

whats tha got to do wid out
12. I'm glad you only did the first three, because I've just noticed you messed up the other two...

Well, they're all square numbers, doesn't that help?
13. (Original post by xxclairexx100)
when i dived them by 15 i get
2x2 = 15 = 15/15 = 1
3x3 = 60 = 60/15 = 4
4x4 = 135 = 135/15 = 9

whats tha got to do wid out
Are you sure you're 5x5 and 6x6 are right? cos they should be sqaure numbers
14. im so confused
15. As I just said, she messed up the other two. I did it myself though, a minute ago, so it's easily done.

http://www.uk-learning.net/t44530.html - Take a look at your other post. All your results there are (or should be) divisible by 9, and give you 1, 4, 9, 16, 25... there's a pattern emerging.
16. (Original post by xxclairexx100)
im so confused
1, 4 and 9 are all sqaure numbers.
So to continue in the same trend, 5x5 = 240/15 = 16 (next square number)
6x6 = 375/15 = 25 (next square number)

so are you sure the differences for N=5, and N=6 are 365 and 540, and not 240 and 375
17. yer but my other results ended up the formula being
(3n)^2 ....that has nothing to do wid 9
18. (3n)² = 9n².
19. thnx for ur help but i just dunt get it
sorry
20. Right... I'll work through the 9x9 grids with you, and show you how I got it, and hopefully you'll be able to do the same with 15x15.

2x2 = 9 diff
3x3 = 36 diff
4x4 = 81 diff
5x5 = 144 diff

All of those numbers divide by 9, so...

9/9 = 1
36/9 = 4
81/9 = 9
144/9 = 16

The sequence you have is the sequence of square numbers.

2x2 ==> 1² = 1 ==> 9
3x3 ==> 2² = 4 ==> 36
4x4 ==> 3² = 9 ==> 81
5x5 ==> 4² = 16 ==> 144

Notice something? The size of the grid is always one bigger than the number I've squared.

In words... the length of the grid is one bigger than the number whose square multiplied by nine gives me your result. (Read that a few times if you don't get it.)

Algebraically:
NxN ==> (N-1)² ==> 9(N-1)².

That's your answer. Tell me if you don't understand bits of it.

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Updated: May 29, 2004
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