symmetric_fizzbuzz.py

def cycle(elems):
	mapping = { elems[i]: elems[(i + 1) % len(elems)] for i in range(len(elems)) }
	return lambda e: mapping[e] if e in mapping else e

def compose(f, g):
	return lambda e: f(g(e))

def cmp_list(a, b):
	return all(a[i] == b[i] for i in range(len(a)))

def cmp_order(f, g, seq):
	f_seq = seq
	g_seq = seq
	while True:
		f_seq = list(map(f, f_seq))
		g_seq = list(map(g, g_seq))
		f_id = cmp_list(f_seq, seq)
		g_id = cmp_list(g_seq, seq)
		if f_id or g_id:
			return f_id and g_id

def fizzbuzz(i):
	cycle_i = cycle(range(i))
	buf = []
	if cmp_order(cycle_i, compose(cycle_i, cycle(range(i, i + 3))), range(i + 3)):
		buf.append('fizz')
	if cmp_order(cycle_i, compose(cycle_i, cycle(range(i, i + 5))), range(i + 5)):
		buf.append('buzz')
	print(''.join(buf) if len(buf) else i)

for i in range(1, 100):
	fizzbuzz(i)