# Python | Three element sum in list

The problem of getting the number of pairs that lead to a particular solution has been dealt many times, this article aims at extending that to 3 numbers and discussing several ways in which this particular problem can be solved. Let’s discuss certain ways in which this can be performed.

Method #1 : Using Nested loops

This is the naive method in which this particular problem can be solved and takes outer loop to iterate for each elements and inner loop checks for the remaining difference adding the pairs to the result.

 `# Python3 code to demonstrate ` `# 3 element sum  ` `# using nested loops ` ` `  `# initializing list ` `test_list ``=` `[``4``, ``1``, ``3``, ``2``, ``6``, ``5``] ` ` `  `# initializing sum  ` `sum` `=` `9` ` `  `# printing original list ` `print``(``"The original list : "` `+` `str``(test_list)) ` ` `  `# using nested loops ` `# 3 element sum  ` `res ``=` `[] ` `for` `i ``in` `range``(``0``, ``len``(test_list)``-``2``): ` `    ``for` `j ``in` `range``(i ``+` `1``, ``len``(test_list)``-``1``): ` `        ``for` `k ``in` `range``(j ``+` `1``, ``len``(test_list)): ` `            ``if` `test_list[i] ``+` `test_list[j] ``+` `test_list[k] ``=``=` `sum``: ` `                ``temp ``=` `[] ` `                ``temp.append(test_list[i]) ` `                ``temp.append(test_list[j]) ` `                ``temp.append(test_list[k]) ` `                ``res.append(``tuple``(temp)) ` ` `  `# print result ` `print``(``"The 3 sum element list is : "` `+` `str``(res)) `

Output :

```The original list : [4, 1, 3, 2, 6, 5]
The 3 sum element list is : [(4, 3, 2), (1, 3, 5), (1, 2, 6)]
```

Method #2 : Using `itertools.combination()`
This particular problem can also be done in a concise manner using the inbuilt function of function. The combination function finds all the combination taking K arguments leading to particular sum.

 `# Python3 code to demonstrate ` `# 3 element sum  ` `# using itertools.combination() ` `from` `itertools ``import` `combinations ` ` `  `# function to get the sum  ` `def` `test(val): ` `    ``return` `sum``(val) ``=``=` `9` ` `  `# initializing list ` `test_list ``=` `[``4``, ``1``, ``3``, ``2``, ``6``, ``5``] ` ` `  `# initializing sum  ` `summation ``=` `9` ` `  `# printing original list ` `print``(``"The original list : "` `+` `str``(test_list)) ` ` `  `# using itertools.combination() ` `# 3 element sum  ` `res ``=` `list``(``filter``(test, ``list``(combinations(test_list, ``3``)))) ` ` `  `# print result ` `print``(``"The 3 sum element list is : "` `+` `str``(res)) `

Output :

```The original list : [4, 1, 3, 2, 6, 5]
The 3 sum element list is : [(4, 3, 2), (1, 3, 5), (1, 2, 6)]
```

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