Maths help needed

[marinyork]

In a grid that is 10x10 the formula is 10(3x2 -3 -2 +1). Note it doesn't matter what number it starts on.

 

[marinyork]

1 2 this leads to 2x21- 1x22 = 20
11 12
21 22

is identical to

88 89 90
98 99 100

because 90x98=8820
and 88x100=8800

So a 3x2 is the same as a 2x3 anywhere at all within a 10x10 grid.

 

[Milo]

Well using my previous formula to work out a 10 by 10 grid The way I would do it that I understand is this.
9squared = 81 x 10 = 810
So in the 10x10 grid the difference would be 810.
Is it possible to explain the formula for example on a 6x5 grid in a way similer to this. I really appreciate all this help but some of these explainaitions make me want to dive head first out my window.

 

[marinyork]

You mean the total size of the grid is 6x5 i.e.

1 2 3 4 5
6 7 8 9 10
11 ... 15
16 ... 20
21 ... 25
26 ... 30

or do you mean just 6 x 5 within the 10 x 10 grid you started with?

 

[marinyork]

Right a grid with 6 rows and 5 columns within a 10x10 grid.

1 2 3 4 5
11 12 13 14 15
21 22 23 24 25
31 32 33 34 35
41 42 43 44 45
51 52 53 54 55

this leads to 10(6x5 - 6- 5 +1) = 10x20 = 200
we get 51x5 - 1x55 = 255-55 = 200

2 3 4 5 6
12 13 14 15 16
22 23 24 25 26
32 33 34 35 36
42 43 44 45 46
52 53 54 55 56

52x6-2x56 = 312-112= 200

 

[Milo]

Just 6 by 5 in the grid I started with there is only one grid

 

[marinyork]

Just 6 by 5 in the grid I started with there is only one grid

because if there were grids of other sizes there are formulas for those .
See above for your question though.

 

[Milo]

I think I kinda get it it now so if I was doing a 4x3 grid I would do 4x3 -4+1?

 

[marinyork]

Times by 10 yes.

 

[marinyork]

For some other info you may find helpful compare

1 2 3
11 12 13

with

1 2
11 12
21 22

2x21-1x22 = 20 and so does the other grid. Why is this?
the difference between 22 and 13 is 9 in and the difference between 3x11 and 2x21 is 9 which is why it doesn't matter whether it is a 3x2 or 2x3 grid. Kilie has written columns x rows in his formula. Basically it doesn't matter though.

 

[Milo]

HA ha Eureka
*dances a jig*

 

[killiekosmos]

Assuming you start at number N with a box X by Y. The corners are
Top left: N Top Right N + (X-1)
Bottom left: N + 10(Y-1), Bottom right N + 10(Y-1) + (X-1)
Top left * Bottom right is: NN + 10NY -11N + NX

Top right * Bottom left is: NN + 10NY-11N + NX + 10XY -10X - 10Y + 10

Difference is: 10XY -10X-10Y+10

= 10(XY-X-Y + 1) QED

Now can you come and do my garden?

I gave you the answer on page 1!

 

[marinyork]

I gave you the answer on page 1!

That was merely for a particular type of 10x10 grid, we've so moved beyond that and miloat has thankfully finished it.

 

[killiekosmos]

Did I pass or have I got another resit?

 

[ColinJ]

I worked out the formula, and was about to post it when I thought "Oh FFS I've just spent my time thinking about this and all because miloat didn't bother to pay attention in class!" So, I didn't bother either...

On a more serious note - I don't think it really helps to just hand someone the answer to a problem. My sister phoned me up one evening because she couldn't work out how to do her daughter's homework for her. I told her that I could do it, but I wasn't going to. If my niece wanted to discuss the problem, I'd gladly help her understand how to go about solving it.