Triangle Puzzle

triangle.py

import itertools

def triangle(base):
    stack = [base]
    while len(stack[-1])>1:
        stack.append([abs(i-j) for i,j in zip(stack[-1],stack[-1][1:])])
    return stack

def check(triangle):
    return len(set(itertools.chain(*triangle))) == sum(range(len(triangle)+1))

def bases(layers):
    max = sum(range(layers+1))
    rev = set()
    for c in itertools.combinations(range(2,max-1),layers-2):
        for d in (max-1,1):
            for p in itertools.permutations(c+(max,d)):
                if p not in rev:
                    rev.add(tuple(reversed(p)))
                    if check(triangle(p)):
                        yield p
    print("Count: ",len(rev))

def guess(layers):
    for i in bases(layers):
        print(triangle(i))

while True:
    guess(int(input("Number of layers? ")))

##    Number of layers? 2
##    [(3, 2), [1]]
##    [(3, 1), [2]]
##    Count:  2
##    Number of layers? 3
##    [(2, 6, 5), [4, 1], [3]]
##    [(6, 2, 5), [4, 3], [1]]
##    [(4, 6, 1), [2, 5], [3]]
##    [(4, 1, 6), [3, 5], [2]]
##    Count:  18
##    Number of layers? 4
##    [(8, 3, 10, 9), [5, 7, 1], [2, 6], [4]]
##    [(8, 10, 3, 9), [2, 7, 6], [5, 1], [4]]
##    [(6, 10, 1, 8), [4, 9, 7], [5, 2], [3]]
##    [(6, 1, 10, 8), [5, 9, 2], [4, 7], [3]]
##    Count:  504
##    Number of layers? 5
##    [(6, 14, 15, 3, 13), [8, 1, 12, 10], [7, 11, 2], [4, 9], [5]]
##    Count:  26400
##    Number of layers? 6
##    Count:  2203200