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    <p><em>Permutations</em> are about taking an ordered set of things and moving these things around (i.e. changing order). Your question is about <em>combinations</em> of things from your list.</p> <p>Now, an easy way of enumerating combinations is by mapping entries from your list to bits in a number. For example, lets assume that if bit #0 is set (i.e. 1), then number <code>lst[0]</code> participates in the combination, if bit #1 is set, then <code>lst[1]</code> participates in the combination, etc. This way, numbers in range <code>0 &lt;= n &lt; 2**(len(lst))</code> identify all possible combinations of <code>lst</code> members, including an empty one (<code>n = 0</code>) and the whole <code>lst</code> (<code>n = 2**(len(lst)) - 1</code>).</p> <p>You need only combinations of 2 items or more, i.e. only those combination IDs that have at least two nonzero bits in their binary representation. Here is how to identify these:</p> <pre><code>def HasAtLeastTwoBitsSet(x) : return (x &amp; (x-1)) != 0 # Testing: &gt;&gt;&gt; [x for x in range(33) if HasAtLeastTwoBitsSet(x)] [3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31] </code></pre> <p>Next step is to extract a combination of list members identified by a combination id. This is easy, thanks to the power of list comprehensions:</p> <pre><code>def GetSublistByCombination(lst, combination_id) : res = [x for (i,x) in enumerate(lst) if combination_id &amp; (1 &lt;&lt; i)] return res # Testing: &gt;&gt;&gt; GetSublistByCombination([0,1,2,3], 1) [0] &gt;&gt;&gt; GetSublistByCombination([0,1,2,3], 3) [0, 1] &gt;&gt;&gt; GetSublistByCombination([0,1,2,3], 12) [2, 3] &gt;&gt;&gt; GetSublistByCombination([0,1,2,3], 15) [0, 1, 2, 3] </code></pre> <p>Now let's make a generator that produces all sums, together with their string representations:</p> <pre><code>def IterAllSums(lst) : combinations = [i for i in range(1 &lt;&lt; len(lst)) if HasAtLeastTwoBitsSet(i)] for comb in combinations : sublist = GetSublistByCombination(lst, comb) sum_str = '+'.join(map(str, sublist)) sum_val = sum(sublist) yield (sum_str, sum_val) </code></pre> <p>And, finally, let's use it:</p> <pre><code>&gt;&gt;&gt; for sum_str, sum_val in IterAllSums([1,2,3,4]) : print sum_str, sum_val 1+2 3 1+3 4 2+3 5 1+2+3 6 1+4 5 2+4 6 1+2+4 7 3+4 7 1+3+4 8 2+3+4 9 1+2+3+4 10 </code></pre>
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