brute force solution for a math question

q7.py

#coding: utf-8

import sys
import itertools

write = sys.stdout.write

nums = [i for i in range(1, 9+1)]

for hidden in itertools.combinations(nums, 2):
    shown = list(sorted(set(nums) - set(hidden)))
    assert len(shown) == 7
    
    for num_on_blackboard in range(10, 99+1):
        mod_0_stus = 0
        for stu in shown:
            possible_nums = [stu] + list(hidden)
            if all(num_on_blackboard % pn == 0 for pn in possible_nums):
                mod_0_stus += 1
        if mod_0_stus == 5:
            write("hidden = %s\n" % list(hidden))
            write("num on blackboard = %d\n" % num_on_blackboard)
            write("\n")