combinations with python

main.py

from itertools import combinations

SUM = 25
NUMS = [20, 17, 15, 13, 10, 8, 7, 5, 5]


def calc(variant, nums):
    return sum([x for i, x in enumerate(nums) if i in variant])

def check(variant, sum, nums):
    return sum == calc(variant, nums)

def header(nums, w):
    fmt = "%%%is" % w
    print(" ".join([fmt % x for x in nums]))

def format(variant, nums, w):
    fmt = "%%%is" % w
    print(" ".join([fmt % ("x" if i in variant else " ") for i in range(len(nums))]))

def check_combinations(sum, nums, w, found_callback):
    num = 0
    for combination_length in range(1, len(nums) + 1):
        for comb in combinations(range(len(nums)), combination_length):
            if check(comb, sum, nums):
                found_callback(comb, nums, w)
                num += 1
    return num

def work(sum, nums, w=2):
    header(nums, w)
    total = check_combinations(sum, nums, w, format)
    print()
    print("Total combinations found: %i" % total)

if __name__ == "__main__":
    work(SUM, NUMS, 4)

output

$ python main.py 
  20   17   15   13   10    8    7    5    5
   x                                  x     
   x                                       x
        x                   x               
             x         x                    
             x                        x    x
                  x              x    x     
                  x              x         x
                       x    x    x          
                            x    x    x    x

Total combinations found: 9

would run slightly faster if using generators instead of list comph.

sum((x for i, x in enumerate(nums) if i in variant))

 print(" ".join((fmt % ("x" if i in variant else " ") for i in range(len(nums)))))