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## #1 2012-01-10 22:25:40

anna_gg
Member
Registered: 2012-01-10
Posts: 232

### Make 1000 using 6 8's

Use number 8 6 times to make 1000.
You can only use +, -, *, /, square root and parenthesis ().
No factorials, 3rd root or any other numbers.

Thank you!!!

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## #2 2012-01-11 00:52:13

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Make 1000 using 6 8's

Hi anna_gg;

Welcome to the forum! Do you know whether this has an answer or not?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #3 2012-01-11 01:29:29

anna_gg
Member
Registered: 2012-01-10
Posts: 232

### Re: Make 1000 using 6 8's

It does, but I don't know it! All my attempts end up in using 7 8's or more!

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## #4 2012-01-11 01:39:19

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Make 1000 using 6 8's

Yes, there are lots of solutions for 8 8's and perhaps for 7 8's also. But I have never seen one for 6 8's.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #5 2012-01-11 03:09:56

bob bundy
Registered: 2010-06-20
Posts: 8,322

### Re: Make 1000 using 6 8's

hi anna_gg and bobbym

I've got some 7 eights solutions.  But 6 is still eluding me.

Bob

The five weighings problem is getting very complicated.

I'm doing things like balance 2 unknowns against 1.

If they balance then they must be (10,20,30) or (10,30,40) or (10, 40,50) or (20,30,50)

If the two go down then (10,20,40) or (10,20,50) or (10,30,50)

If not then there's loads of possibilities eeekkk.

Depending on which, try other balance possibilities.

The total map of alternatives is very large!

OR

(Im)Balance any pair and call them v and w so that v<w

(Im)Balance another pair and call them x and y so that x < y.

Then try w against x.  Again lots of possibilities.

Cannot find a simple, elegant way to tackle this.

Last edited by bob bundy (2012-01-11 03:12:06)

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #6 2012-01-11 07:08:44

bob bundy
Registered: 2010-06-20
Posts: 8,322

### Re: Make 1000 using 6 8's

hi anna_gg

Bob

Last edited by bob bundy (2012-01-11 07:11:21)

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #7 2012-01-11 09:48:40

anna_gg
Member
Registered: 2012-01-10
Posts: 232

### Re: Make 1000 using 6 8's

We are only allowed to use decimals in the form 8.8, not .8, as this assumes leading zeros
Otherwise, another like that would be 888/.888.

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## #8 2012-01-12 02:12:48

bob bundy
Registered: 2010-06-20
Posts: 8,322

### Re: Make 1000 using 6 8's

hi anna_gg

Please would you post the exact wording in the original question.

I'm 'clutching at straws' now.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #9 2012-01-12 02:18:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Make 1000 using 6 8's

Hi;

I have done a large computer search for some answer, also a search of the available literature for these type problems. I am coming up dry.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #10 2012-01-12 02:22:05

benice
Member
Registered: 2010-06-10
Posts: 114
Website

### Re: Make 1000 using 6 8's

1000 = 10^3

10 = 8 + sqrt( sqrt(8+8) )
3 = sqrt(8 + 8/8)

Last edited by benice (2012-01-12 02:22:58)

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## #11 2012-01-12 02:28:18

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Make 1000 using 6 8's

Hi;

Are exponents allowed? I thought they were not.

Hi Benice;

If they are then nice solution!

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #12 2012-01-12 02:46:00

anna_gg
Member
Registered: 2012-01-10
Posts: 232

### Re: Make 1000 using 6 8's

Awesome! Thanks!!!

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## #13 2012-01-12 02:53:06

bob bundy
Registered: 2010-06-20
Posts: 8,322

### Re: Make 1000 using 6 8's

It is a nice solution.

But I thought you weren't allowing powers.

That's why I asked for the exact wording.

So is this question done now?

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #14 2012-01-12 02:57:03

anna_gg
Member
Registered: 2012-01-10
Posts: 232

### Re: Make 1000 using 6 8's

Not sure about powers; I must confirm this with the friend who gave me the problem.
Either way, I could not go that close myself!

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## #15 2012-01-12 03:02:11

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Make 1000 using 6 8's

Hi anna_gg;

If it does not include powers can you have your friend clearly state what is good and what is not?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #16 2012-01-12 08:20:55

anna_gg
Member
Registered: 2012-01-10
Posts: 232

### Re: Make 1000 using 6 8's

Confirmed that powers are allowed!

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## #17 2012-01-12 11:25:23

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Make 1000 using 6 8's

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #18 2012-01-13 08:30:09

anna_gg
Member
Registered: 2012-01-10
Posts: 232

### Re: Make 1000 using 6 8's

Thank you all for your help!!

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