Make 1000 using 6 8's

anna_gg · 2012-01-10 22:25:40

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!!!

bobbym · 2012-01-11 00:52:13

Hi anna_gg;

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

anna_gg · 2012-01-11 01:29:29

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

bobbym · 2012-01-11 01:39:19

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.

Bob · 2012-01-11 03:09:56

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 (2012-01-11 03:12:06)

Bob · 2012-01-11 07:08:44

hi anna_gg

Bob

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

anna_gg · 2012-01-11 09:48:40

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.

Bob · 2012-01-12 02:12:48

hi anna_gg

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

I'm 'clutching at straws' now.

Bob

bobbym · 2012-01-12 02:18:38

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.

benice · 2012-01-12 02:22:05

1000 = 10^3

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

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

bobbym · 2012-01-12 02:28:18

Hi;

Are exponents allowed? I thought they were not.

Hi Benice;

If they are then nice solution!

anna_gg · 2012-01-12 02:46:00

Awesome! Thanks!!!

Bob · 2012-01-12 02:53:06

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

anna_gg · 2012-01-12 02:57:03

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!

bobbym · 2012-01-12 03:02:11

Hi anna_gg;

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

anna_gg · 2012-01-12 08:20:55

Confirmed that powers are allowed!

bobbym · 2012-01-12 11:25:23

Hi;

Then I guess this question is closed unless you want more of them.

anna_gg · 2012-01-13 08:30:09

Thank you all for your help!!

Math Is Fun Forum

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

Make 1000 using 6 8's

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

Re: Make 1000 using 6 8's

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

Re: Make 1000 using 6 8's

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

Re: Make 1000 using 6 8's

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

Re: Make 1000 using 6 8's

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

Re: Make 1000 using 6 8's

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

Re: Make 1000 using 6 8's

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

Re: Make 1000 using 6 8's

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

Re: Make 1000 using 6 8's

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

Re: Make 1000 using 6 8's

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

Re: Make 1000 using 6 8's

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

Re: Make 1000 using 6 8's

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

Re: Make 1000 using 6 8's

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

Re: Make 1000 using 6 8's

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

Re: Make 1000 using 6 8's

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

Re: Make 1000 using 6 8's

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

Re: Make 1000 using 6 8's

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

Re: Make 1000 using 6 8's

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