Bead Maze

bead_maze.py

#!/usr/bin/env python3

from functools import lru_cache

@lru_cache(maxsize=1024)
def combinations(beads, low_points):
	if low_points == 1:
		return 1
	return sum(combinations(n, (low_points - 1)) for n in range(0, (beads + 1)))

print('Blue  - 7 beads, 3 lows = {}'.format(combinations(7, 3)))
print('Red   - 8 beads, 5 lows = {}'.format(combinations(8, 5)))
print('Green - 6 beads, 3 lows = {}'.format(combinations(6, 3)))
print('Abacus - 10 beads, 2 lows = {}'.format(combinations(10, 2)))
print('Abacus - 10 beads, 3 lows = {}'.format(combinations(10, 3)))
print('Abacus - 10 beads, 4 lows = {}'.format(combinations(10, 4)))