Maths help needed

[punkypossum]

?????????????????????????????

 

[mickle]

?????????????????????????????

Yeah me too!

 

[Milo]

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A box is drawn round four numbers

Find the product of the top left number and the bottem right number in the box.
Do the same for the top right and bottom left numbers
Calculate the difference between these products
Investigate further.
Thats the heading sheet I have the formulea for grids that are 2x2 3x3 etc.
which is 10 (n-1) cubed
Where N is the grid size you are trying to find the differnce in -1 represents the previous number that you must use so you would use 6 as N if you wanted to find the difference in a 7x7 grid.
So for example If I wanted to find out the differnce in a 6x6 grid I would use the following sum.

5 squared = 25x10 = 250 difference
So in a 6x6 grid the difference would be 250.
geddit?

 

[mickle]

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A box is drawn round four numbers

Find the blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number blah blah blah blah blah blah blah blah blah blah blah number.

geddit?

No, sorry, I just can't see it.

 

[Milo]

Tis only mere gcse work slacker :

 

[Milo]

I can talk ive had a number block on the second bit and the deadlines monday.

 

[bonj2]

A box is drawn round four numbers

Find the product of the top left number and the bottem right number in the box.
Do the same for the top right and bottom left numbers
Calculate the difference between these products
Investigate further.
Thats the heading sheet I have the formulea for grids that are 2x2 3x3 etc.

right, sorry to be pedantic miloat but a grid that's 3x3 etc isn't a box drawn round 4 numbers.
What I'm getting at, is that it seems that while in the case of a square box there are TWO variables, the start square and the side length, in the case of a non-square box there are THREE variables - start number, box width, AND box height. Therefore the product of TLxBR-TRxBL etc will have to take into account ALL of those THREE variables in that case.

Seriously miloat the best tip I can give you in maths is understand how many variables you've got, and list them together with what they mean. if we're on the same understanding as to how many variables there are, then we can go from there...it's a logical step by step process, you won't just come up with the answer in your head in a flash of glory, no-one will, we've got to work it through.

 

[bonj2]

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e.g. on that box, start square = 3, side length = 2.

on this one
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you can define the box by start square = 36, side length = 4.

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however on this one you need to know start square = 62, length = 6, and height = 3. Can you see how you need ALL these pieces of information to define that box? Therefore those three variables will obviously need to all form part of the solution to how you arrive at 62x87 - 67x82.

 

[Milo]

What I copyed out is word by word what the heading sheet says bonj.
this is what results I havde so far.
3x2 grid - difference 20
4x3 grid differnce = 60
5x4 grid = 120
6x5 grid = 200
7x6 grid = 300
Sorry bonj your losing me there.

 

[Milo]

Im half inclined just to put nonsense in bold letters repeatedly over the last page I just cant be arsed.
God knows what this bull is suppose to teach me.
I spent 5 hours yesterday using trail and improvement to find out a formula.
Did I get one Did i ****

 

[marinyork]

Don't panic, all the information is there miloat, we'll just explain it to you.

 

[bonj2]

What I copyed out is word by word what the heading sheet says bonj.
this is what results I havde so far.
3x2 grid - difference 20
4x3 grid differnce = 60
5x4 grid = 120
6x5 grid = 200
7x6 grid = 300
Sorry bonj your losing me there.

right, ok.
say,
W = width of the grid
H = height of the grid
S = starting number of the grid.
With me so far? ok, now we've got the hang of assigning letters to variables, let's let:
TL = top left
TR = top right
BL = bottom left
BR = bottom right.
OK? Now we can start to do formulas.
so:
TL = S. (that one's obvious.)
TR = S + W - 1.
BL = S + 10(H - 1)
BR = S + W - 1 + 10(H - 1)

so top right x bottom left:
TR.BL = (S + W - 1) (S + 10(H-1))
= S² + 10S(H-1) + S(W - 1) + 10(W-1)(H-1)
= S² + S(W - 1 + 10H - 10) + 10(W-1)(H-1)
giving you a quadratic equation in S. So for a 2x3 grid (2 wide and 3 high) you've got W = 2, H = 3, therefore:
TR.BL = S² + (30 - 10 + 2 - 1)S + 10(1)(2)
TR.BL = S² + 21S + 20
see?

now, for top left x bottom right,
TL.BR = S (S + W - 1 + 10(H - 1))
= S² + S(W - 1 + 10H - 10)
so for our 2x3, as before W = 2, H = 3
TL.BR = S² + S(2 - 1 + 30 - 10)
TL.BR = S² + 21S

so for a grid starting on 13 using the above formulas, TL =13, TR=14, BL=33, BR=34.
so TR.BL = 13² + 21x13 + 20
= 169 + 273+20 = 462
to check it, 14x33 = 462.

TL.BR = 13² + 21x13 = 169+273 = 442
to check it, 13x34 = 442.

Now look at the above foumulas in bold and compare them - see how you can use them to come up with a much simpler formula for TR.BL - TL.BR. If i'm right in guessing, I think it's this much simpler formula for TR.BL - TL.BR which is what they want out of you, and the fact that it's much simpler is why they've asked what is the DIFFERENCE between the products of opposite corners.

 

[Milo]

Im trying here but this is way way more complex explaination than what we got at college.
Give me 20 mins

 

[marinyork]

Just look at kiliekosmos's formula too. I do seem to have confused the issue slightly I think devising 4 different kinds of tables. Miloat if you do what kiliekosmos and bonj has done you will find for your table that

(a) it works for any grid by putting in X=whatever, Y=whatever. NB m x n and n x m grids come up with the same results but it's slightly more work to demonstrate this.
( the starting number doesn't matter. You demonstrate this by among other methods using algebra as kiliekosmos and bonj has. Then substitute in a few numbers like bonj has to demonstrate that it works.

Your coursework is basically wanting you to investigate it algebraically as kiliekosmos has done and then substitute a few values in to check as bonj has. If you were wanting to be really cheeky you could investigate what affect other grids are on the formulas as I have done or investigate why a m x n grid comes up with the same answer as a n x m grid in your case i.e. it'll get you more marks perhaps.

 

[Milo]

I just want to get the form#
ulea for the 3x2 style grids and never ever ever ever have to do anything like this ever ever ever again.
Sorry Bonj your still losing me a bit.