gistfile1.py

import random

STUDENTS = 16
PROJECTS = 10
STUDENTS_PER_PROJECT = 4


def sim():
	all_students = range(STUDENTS)

	worked_with = {x: set() for x in range(STUDENTS)}

	for x in range(PROJECTS):
		random.shuffle(all_students)
		for group in range((STUDENTS//STUDENTS_PER_PROJECT)+1):
			team = all_students[(group * STUDENTS_PER_PROJECT): ((group+1) * STUDENTS_PER_PROJECT)]
			for member in team:
				for partner in team:
					worked_with[member].add(partner)

	for student in worked_with:
		if len(list(worked_with[student])) != STUDENTS:
			return False

	return True

def run_sims(n=100):
	true, false = 0., 0.
	for x in range(n):
		if sim():
			true += 1
		else:
			false += 1
	print "{} true, {} false, {} percent".format(true, false, (true/(true+false)))

run_sims(10000)