Wanted to know what lego technic gears I needed to make something rotate once a year... guess I found it :)

gear_ratio_finder.py

from collections import defaultdict

def get_gears_for_ratio(ratio, gears, maxdepth=10):
    shortestpath = dict()
    shortestpath[1] = list()
    expanded = defaultdict(lambda: False)
    depth = 0
    while ratio not in shortestpath.keys():
        depth +=1
        if depth > 14:
            return False, shortestpath
        for startratio in list(shortestpath.keys()):
            if expanded[startratio]:
                continue
            expanded[startratio] = True
            path = shortestpath[startratio]
            for front in gears:
                for back in gears:
                    reached = startratio * (back/front)
                    if reached not in shortestpath:
                        shortestpath[reached] = path + [(front, back)]
    return True, shortestpath


lego_technic_gears = [8, 12, 14, 16, 20, 24, 36, 40]
searching = 3.5
foundit, dictionary = get_gears_for_ratio(3.5, lego_technic_gears, maxdepth=5)
if foundit:
    print(dictionary[searching])