Generate a valid equation using user-specified numbers

Python 2.7 (284), Python 3.x (253)

from __future__ import division #(Remove for Python 3.x)
from itertools import *
a=raw_input().split()
for i in permutations(a[:-1],5):
 for j in product('+-*/',repeat=5):
  for k,l in combinations(range(1,12,2),2):
   d=''.join(sum(zip(i,j),()))[:-1];d='('+d[:l]+')'+d[l:]
   if eval(d)==int(a[-1]):print d;b

It gives an error (calling unknown function b) on solution.

Basically, it's a gigantic brute force. It takes in the input, splits it by its spaces (1 2 -> [1,2]), and then permutes through that list. With every permutation, it will iterate through all possible strings of length 5 using the characters +-*/. With each of those iterations, it will generate the combinations of length 2 of the list [1,3,5,7,9,11], interweave the permutation and the string together (12345 *-/+- -> 1*2-3/4+5-), and put in the parentheses. Finally, it will evaluate it, and if the answer and equation are true, then it prints the equation and stops.

This is horribly inefficient, about O(n!/(n-5)!)=O(n^5), but it runs in a reasonable time for the test inputs.

Scala 368:

The 2nd g=-Line is more easy to test, the first is flexible to take command arguments, and both are of equal length, so I only count from the second one - remove it to do args passing:

val g=(args.map(_.toDouble))
val g=Array(3,9,2, 1, 6, 87)
val k="+*/-DQ"
val i=(0 to 5)
val f:Seq[(Double,Double)=>Double]=Seq(_+_,_*_,_/_,_-_,(a,b)=>b-a,(a,b)=>b/a)
val h=g.init.permutations;
for(j<-h;o<-i;p<-i;q<-i;r<-i;z=try{f(r)(f(q)(f(p)(f(o)(j(0),j(1)),j(2)),j(3)),j(4))}catch{case _ => 0}
if(z==g(5)))printf("(((%d%c%d)%c%d)%c%d)%c%d=%d\n",j(0),k(o),j(1),k(p),j(2),k(q),j(3),k(r),j(4),g(5))

Sample output (you might have a question right now - just a moment):

(((5+7)/1)+6)*3=54
(((5-7)D1)*6)*3=54
(((5D7)+1)*6)*3=54
(((5+7)+6)Q1)Q3=54

What about this 5D7 thing? D1? Is it hex? There is Q1, Q3 - what's that.

Sir_Lagsalot allowed new basic operations in the spirit of the challenge, and yes, these are basic operations, Delta and Quotient.

They are different from a/b and a-b in that aQb means b/a and aDb means b-a. Let's call it the Ukrainian notation.

So

(((5-7)D1)*6)*3=54

means

((1-(5-7))*6)*3=54
 (1-(-2))*6*3
   3*6*3 = 18*3=54

To the more interesting question of the how and why: In the beginning I got mad about the possibilities to place the parentheses, and whether (a+b)-c = a+b-c = (a+b-c) = ((a+b)-c) = (b+a)-c and so on. You can get mad over this question, but if you write down the possible parenthesis combinations, you sometimes throw away the scratch sheet and face the fact: You always perform 4 operations between 5 values, and you always start with one of them. If the pattern is always (((_x_)x_)x_)x_ ?= _ (x being one of the 4 operators) and allow the opposite direction ( x b) and (b x a), you addressed every possibility.

Now for a+b and a*b we don't need no opposite direction, they are commutative. So I invented the D and Q operator, which just switch the direction. I now have 2 operators more, but don't need to switch direction. Well - it is done in the function Sequence:

 (a,b)=>b-a,(a,b)=>b/a

My for-comprehension takes the values from the Array g, and distributes them on a to e, then I pick 4 indexes to pick the function and later the (only by index) associated operator symbol. I have to catch div/0 errors, since subtraction can lead to zeros, while the sample input data doesn't contain a 0.