Math Is Fun Forum

sam123

Guest

grid pattern

my little brother asked for help on maths homework but i haven't a clue.

theres a 10 x 10 grid with numbers 1-100. you have to draw a box around 4 random numbers, multiply diagonally both ways then find the difference. he has found that this is always 10 but dosn't understand why. he now has to come up with a formula/equation but doesn't know how to start.

if someone could show me how to start him off that would be great.

many thanks.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: grid pattern

I'm not sure what the task is. Could you try to explain it in more detail, possibly with an image as well?

---

Why did the vector cross the road?
It wanted to be normal.

sam123

Guest

Re: grid pattern

grid :
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
11, 12, etc. up to 100.

draw a 2 x 2 box as follows:

----------
1, 2     
11, 12 
-----------

multiply top left by bottom right, and top right by bottom left:
1 x 12 = 12
2 x 11 = 22
find difference: 22 - 12 = 10.

he has found that wherever he puts the box the diference is always 10, but has been told to show it algerbraically and i just don't remember how to even start.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: grid pattern

Brief explanation:

Last edited by JaneFairfax (2007-03-23 01:20:29)

numen

Member

Registered: 2006-05-03

Posts: 115

Re: grid pattern

You see, however you pick your 2 x 2 box, all the numbers will have a relation to eachother according to your grid. Let the first number be called A, then the next number will be A+1, A+2, A+3,... filling up your entire grid.

Now, however you pick your square doesn't matter. Let the number in the first  row and first column (of your square) be called x, then the next one is always x+1. The bottom ones in your square will always be x+10 and x+11, such as

x        x+1
x+10  x+11

Do you see why?

Do you know how to proceed from here? All you have to do know is to set up the expression you stated, multiplying diagonally and finding the difference.

(x+1)*(x+10) - x*(x+11) = ??

Edit: I see Jane already posted, but maybe an explanation will help =P

Last edited by numen (2007-03-23 01:34:37)

---

Bang postponed. Not big enough. Reboot.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: grid pattern

Oooh, I see now. I didn't realise that the 4 random boxes had to form a square like that.

Is this just a homework, or one of those project things that you need to extend on once you find the answer to the original problem? I remember having to do something like this and doing all kinds of crazy things like generalising the size of the grid and of the square in the grid and I ended up with a massive formula that had around 4 variables in it. Great fun. Anyway, if it is one of those, feel free to ask for more help if you need it.

---

Why did the vector cross the road?
It wanted to be normal.

sam123

Guest

Re: grid pattern

Thank you all very much that's really helpful.