http://zariski.wordpress.com/2013/08/02/%EC%98%A4%EB%8A%98%EC%9D%98-%EB%B8%8C%EB%A0%88%EC%9D%B8%ED%8B%B0%EC%A0%80/ 문제를 확인하기 위한 코드. 결과적으로 35개의 3으로 이루어진 목록은 나오지만 최종적으로 1만으로 이루어진 데까지는 가지 않는다.

tease.py

# -*- coding:utf-8 -*-

from itertools import combinations
from pprint import pprint

bundle = [51,49,5]
candidates = [bundle]
loop = True
loop_count = 0
largest_member = []

while loop:
    loop_count = loop_count + 1
    max_number_of_members = 0
    max_member = 0

    #if len(largest_member) > 33: candidates = [largest_member]

    #print candidates

    for i,b in enumerate(candidates):
        splitable = False
        if max_number_of_members < len(b):
            max_number_of_members = len(b)
            largest_member = b

        # 나눌 수 있으면
        for key,val in enumerate(b):
            if val % 2 == 0:
                splitable = True
                # 현재 묶음은 제거
                del candidates[i][key]
                # 나눈 값으로 새 묶음 생성
                candidates[i].append(val/2)
                candidates[i].append(val/2)
                candidates[i].sort()
                if max_member < max(candidates[i]):
                    max_member = max(candidates[i])

        # 나눌 수 없었으면
        if splitable == False:
            # 합해서 다른 묶음 생성
            for c in combinations(b,2):
                _b = list(b)
                _b.remove(c[0])
                _b.remove(c[1])
                _b.append(c[0] + c[1])
                _b.sort()
                candidates.append(_b)
            # 현재 묶음은 제거
            del candidates[i]

    candidates = reduce(lambda x, y: x if y in x else x + [y], candidates, [])
    pprint(candidates)
    print len(candidates), max_number_of_members, max_member, largest_member

    if loop_count >= 1000:
        loop = False
    if len(candidates) == 0:
        loop = False
    if max_number_of_members == 1:
        loop = False