How do I create a program that yields combinations of sums for a single integer?

Question

In python, I want to have my program prompt me to 'Enter number:' and then I will do so. For example, I will enter '5' and in return I want it to find every combination of numbers between 1 and 5, including 1 and 5, that adds up to 5 without repeating any sequences or numbers. So the output of this should be the pairs 1,4 and 2,3. On top of that, I also want it to tell me how many outputs I have, so in this case 2. And I want to make sure that if I input a number higher, say 10, it will yield every combination even if it is larger than a pair, so it would yield 1,2,3,4 as one of the outputs and 1,9 as another, etc.

Answer 1

There you go, because I like playing with itertools, but yes, next time try something by yourself :

import itertools

val = int(input())
r = range(val)[1:]
res = []    
for i in range(len(r)+1):
    res += [list(x) for x in itertools.combinations(r, i) if sum(list(x)) == val]    
print("Solution : %s " % res)
print("Combinations : %s" % len(res))

# For input 10 : 
# Solution : [[1, 9], [2, 8], [3, 7], [4, 6], [1, 2, 7], [1, 3, 6], [1, 4, 5], [2, 3, 5], [1, 2, 3, 4]]
# Combinations : 9

This method is kind of a bruteforce, you could probably be much faster using maths.