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**coolcat23****Member**- Registered: 2006-06-21
- Posts: 553

I need help on the following question:

place numbers1-9 on the lines so that all the equations are accurate

__ divided by _ = _ - _ = _ + _ = _ x _

PLEASE HELP!!!!!!!!!!!!!!!!!!!

The world revolves around me. Deal with it.

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**luca****Guest**

just try it out-

__ divided by _ = _ - _ = _ + _ = _ x _

1,2,3,4,5,6,7,8,9

its impossible, ill proove it by exhaustion

lets just stick to the division and multiplication

the division will always be <= 9, (max / min = 9) and has to be an integer to satisfy the rest of the equalities

(im changing order to division = multiplication = addition = subtraction)

9/1 = fail (can only do 3x3, but cant do that, using same number)

8/1 = 4x2 = 2+6 = fail (cannot use 9-1, 1 is used)

8/1 = 4x2 = 3+5 = fail (cannot use 9-1, 1 is used)

7/1 = fail (can only do 7x1, both are taken)

6/1 = 3x2 = fail (cannot get an addition with other numbers)

5/1 = fail (can only do 5x1, both are taken)

4/1 = fail (can only do 4x1, both taken, or 2x2, but thats same number)

3/1 = fail (can only do 3x1, both are taken)

2/1 = fail (can only do 2x1, both are taken)

9/3 = fail (can only get 3 using 3)

8/4 = 2x1 = fail (cannot get 2 = 1+1, same number, and 1 is already taken anyways)

8/2 = 4x1 = fail (cannot do 1+3, 1 is taken, 2+2 is using same number 3 times)

6/3 = 2x1 = fail (cannot get 2 = 1+1, same number, and 1 is already taken anyways)

6/2 = 3x1 = fail (can only get 3, using 3)

4/2 = fail (can only get 2 using 2)

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

There aren't any solutions if you include 0, either.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

The first solution that exists for starting at 1 is when the highest number is 13:

10 / 1 = 13 - 3 = 4 + 6 = 2 * 5

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Weirdly enough, that's the same for starting at 0.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**coolcat23****Member**- Registered: 2006-06-21
- Posts: 553

I've got it! I think.After a couple of hours trying different things i got this:.

56 divided by 8 = 9 - 2 =3 + 4 =1 x7

The world revolves around me. Deal with it.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Oh, is that what the double underscore was for? Well that changes everything.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

And that is a unique solution. i.e. there aren't any others.

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**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

Ricky wrote:

Oh, is that what the double underscore was for? Well that changes everything.

i was wondering why there was 9 numbers, but 8 places for them

oh, and if you didnt notice, 'luca' is me, when i post, and then realise im not logged in and cant be math to

edit no2

what the? a r * e d, is converted to math?!

*Last edited by MathsIsFun (2006-06-27 09:42:14)*

The Beginning Of All Things To End.

The End Of All Things To Come.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,619

Yeah, coz itz a bit rooood.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**coolcat23****Member**- Registered: 2006-06-21
- Posts: 553

Thanks for all your help!!

The world revolves around me. Deal with it.

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