numbers puzzle two

[jay_shark]

Use the following numbers as often as they appear to give you 1/3 .

The numbers are : 1,1,1,1,1,1,1,1,2,3,3,4,4,5,5,6 using any of the operations +-*/ . I'm not sure how many solutions there are , but I know one method works .

[Alex-db]

white:
<font color="white"> (1+1+1+1+1+1+1+1+2) / (3+3+4+4+5+5+6) </font>

Edited again after note below, I think it was ok, 16 numbers and 15 operators?

[jay_shark]

Not sure I quite follow yours but perhaps you're right .

There are 16 numbers in total . You have 8 addition signs in the numerator and 6 at the bottom .

[Spence]

can this be done logically? Or is it a guess and check kind of thing? If it can be done with a formula, where can I read about it?

[jay_shark]

This one I came up with myself after being inspired by a thread on www.cut-the-knot.com on the ctk exchange forum .

I suppose you just have to look for some kind of pattern like why are 2 and 6 only used once ?

[ddollevoet]

((1+1)/6) + 1/1 - 1/1 + ((1+1)/2) - 3/3 + 4/4 - 5/5 <font color="white"> </font>

[jay_shark]

Cool ddollevoet .

That makes two solutions that i'm aware of .

[DrunkHamster]

(1^8)x [(3.4.5)/(3.4.5)] x (2/6)
unless I've been really stupid...

[NickMPK]

This one is not nearly as clever as the first one.
I'm sure there are a ton of solutions. How about:

(1/3) + (1/2) - (3/6) + 4 - 4 + 5 - 5 + 1 - 1 + 1 - 1 + 1 - 1

[jay_shark]

Very nice solutions to everyone who replied .

I didn't know there were so many answers .