# Solution of;
# Project Euler Problem 84: Monopoly odds
# https://projecteuler.net/problem=84
# 
# In the game, Monopoly, the standard board is set up in the following way:A 
# player starts on the GO square and adds the scores on two 6-sided dice to 
# determine the number of squares they advance in a clockwise direction. 
# Without any further rules we would expect to visit each square with equal 
# probability: 2. 5%. However, landing on G2J (Go To Jail), CC (community 
# chest), and CH (chance) changes this distribution. In addition to G2J, and 
# one card from each of CC and CH, that orders the player to go directly to 
# jail, if a player rolls three consecutive doubles, they do not advance the 
# result of their 3rd roll. Instead they proceed directly to jail. At the 
# beginning of the game, the CC and CH cards are shuffled. When a player lands 
# on CC or CH they take a card from the top of the respective pile and, after 
# following the instructions, it is returned to the bottom of the pile. There 
# are sixteen cards in each pile, but for the purpose of this problem we are 
# only concerned with cards that order a movement; any instruction not 
# concerned with movement will be ignored and the player will remain on the 
# CC/CH square. Community Chest (2/16 cards):Advance to GOGo to JAILChance 
# (10/16 cards):Advance to GOGo to JAILGo to C1Go to E3Go to H2Go to R1Go to 
# next R (railway company)Go to next RGo to next U (utility company)Go back 3 
# squares. The heart of this problem concerns the likelihood of visiting a 
# particular square. That is, the probability of finishing at that square 
# after a roll. For this reason it should be clear that, with the exception of 
# G2J for which the probability of finishing on it is zero, the CH squares 
# will have the lowest probabilities, as 5/8 request a movement to another 
# square, and it is the final square that the player finishes at on each roll 
# that we are interested in. We shall make no distinction between "Just 
# Visiting" and being sent to JAIL, and we shall also ignore the rule about 
# requiring a double to "get out of jail", assuming that they pay to get out 
# on their next turn. By starting at GO and numbering the squares sequentially 
# from 00 to 39 we can concatenate these two-digit numbers to produce strings 
# that correspond with sets of squares. Statistically it can be shown that the 
# three most popular squares, in order, are JAIL (6. 24%) = Square 10, E3 (3. 
# 18%) = Square 24, and GO (3. 09%) = Square 00. So these three most popular 
# squares can be listed with the six-digit modal string: 102400. If, instead 
# of using two 6-sided dice, two 4-sided dice are used, find the six-digit 
# modal string.
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 84
    timed.caller(dummy, n, i, prob_id)
