https://www.popularmechanics.com/science/math/a27415/riddle-of-the-week-34-two-wizards-ride-a-bus/

wizards.py

import functools as ft
import itertools as it
import operator as op

def generate_factors(b, n, smallest_number=1):
	if n == 1:
		yield [b]
	else:
		for i in range(smallest_number, b // 2 + 1):
			for s in generate_factors(b-i, n-1, i):
				yield [i] + s

def duplicate_products(cs):
	seen = set()
	dups = set()
	for c in cs:
		product = ft.reduce(op.mul, c, 1)
		if product in seen:
			dups.add(product)
		seen.add(product)
	return dups

def factors_with_sum(b):
	return map(lambda n: (n, list(generate_factors(b, n))), range(1, b + 1))

def analyze_duplicates(b):
	dup_coords = set()

	for n, cs in factors_with_sum(b):
		dups = duplicate_products(cs)
		for a in dups:
			dup_coords.add((b, n, a))

	return dup_coords

for b in [12, 13, 14]:
	print(b, analyze_duplicates(b))