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The solution @kgoodrick offered is great but I think it is more useful as a generator:

def subset_sum(numbers, target, partial=[], partial_sum=0):
    if partial_sum == target:
        yield partial
    if partial_sum >= target:
        return
    for i, n in enumerate(numbers):
        remaining = numbers[i + 1:]
        yield from subset_sum(remaining, target, partial + [n], partial_sum + n)

list(subset_sum([1, 2, 3, 7, 7, 9, 10], 10)) yields [[1, 2, 7], [1, 2, 7], [1, 9], [3, 7], [3, 7], [10]].

The solution @kgoodrick offered is great but I think it is more useful as a generator:

def subset_sum(numbers, target, partial=[], partial_sum=0):
    if partial_sum == target:
        yield partial
    if partial_sum >= target:
        return
    for i, n in enumerate(numbers):
        remaining = numbers[i + 1:]
        yield from subset_sum(remaining, target, partial + [n], partial_sum + n)

Output:

print(list(subset_sum([1, 2, 3, 7, 7, 9, 10], 10)))
# [[1, 2, 7], [1, 2, 7], [1, 9], [3, 7], [3, 7], [10]]

The solution @kgoodrick offered is great but I think it is more useful as a generator:

def subset_sum(numbers, target, partial=[], partial_sum=0):
    if partial_sum == target:
        yield partial
    if partial_sum >= target:
        return
    for i, n in enumerate(numbers):
        remaining = numbers[i + 1:]
        yield from subset_sum(remaining, target, partial + [n], partial_sum + n)

list(subset_sum([1, 2, 3, 7, 7, 9, 10], 10)) yields [[1, 2, 7], [1, 2, 7], [1, 9], [3, 7], [3, 7], [10]].

The solution @kgoodrick offered is great but I think it is more useful as a generator:

def subset_sum(numbers, target, partial=[], partial_sum=0):
    if partial_sum == target:
        yield partial
    if partial_sum >= target:
        return
    for i, n in enumerate(numbers):
        remaining = numbers[i + 1:]
        yield from subset_sum(remaining, target, partial + [n], partial_sum + n)

list(subset_sum([1, 2, 3, 7, 7, 9, 10], 10)) yields [[1, 2, 7], [1, 2, 7], [1, 9], [3, 7], [3, 7], [10]].

The solution @kgoodrick offered is great but I think it is more useful as a generator:

def subset_sum(numbers, target, partial=[], partial_sum=0):
    if partial_sum == target:
        yield partial
    if partial_sum >= target:
        return
    for i, n in enumerate(numbers):
        remaining = numbers[i + 1:]
        yield from subset_sum(remaining, target, partial + [n], partial_sum + n)

list(subset_sum([1, 2, 3, 7, 7, 9, 10], 10)) yields [[1, 2, 7], [1, 2, 7], [1, 9], [3, 7], [3, 7], [10]].

The solution @kgoodrick offered is great but I think it is more useful as a generator:

def subset_sum(numbers, target, partial=[], partial_sum=0):
    if partial_sum == target:
        yield partial
    if partial_sum >= target:
        return
    for i, n in enumerate(numbers):
        remaining = numbers[i + 1:]
        yield from subset_sum(remaining, target, partial + [n], partial_sum + n)

list(subset_sum([1, 2, 3, 7, 7, 9, 10], 10)) yields [[1, 2, 7], [1, 2, 7], [1, 9], [3, 7], [3, 7], [10]].