<reponame>lcsm29/project-euler<gh_stars>0
# Solution of;
# Project Euler Problem 640: Shut the Box
# https://projecteuler.net/problem=640
# 
# Bob plays a single-player game of chance using two standard 6-sided dice and 
# twelve cards numbered 1 to 12. When the game starts, all cards are placed 
# face up on a table. Each turn, Bob rolls both dice, getting numbers $x$ and 
# $y$ respectively, each in the range 1,. . . ,6. He must choose amongst three 
# options: turn over card $x$, card $y$, or card $x+y$. (If the chosen card is 
# already face down, it is turned to face up, and vice versa. )If Bob manages 
# to have all twelve cards face down at the same time, he wins. Alice plays a 
# similar game, except that instead of dice she uses two fair coins, counting 
# heads as 2 and tails as 1, and that she uses four cards instead of twelve. 
# Alice finds that, with the optimal strategy for her game, the expected 
# number of turns taken until she wins is approximately 5. 673651. Assuming 
# that Bob plays with an optimal strategy, what is the expected number of 
# turns taken until he wins? Give your answer rounded to 6 places after the 
# decimal point.
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 640
    timed.caller(dummy, n, i, prob_id)

# Solution of;
# Project Euler Problem 640: Shut the Box
# https://projecteuler.net/problem=640
# 
# Bob plays a single-player game of chance using two standard 6-sided dice and 
# twelve cards numbered 1 to 12. When the game starts, all cards are placed 
# face up on a table. Each turn, Bob rolls both dice, getting numbers $x$ and 
# $y$ respectively, each in the range 1,. . . ,6. He must choose amongst three 
# options: turn over card $x$, card $y$, or card $x+y$. (If the chosen card is 
# already face down, it is turned to face up, and vice versa. )If Bob manages 
# to have all twelve cards face down at the same time, he wins. Alice plays a 
# similar game, except that instead of dice she uses two fair coins, counting 
# heads as 2 and tails as 1, and that she uses four cards instead of twelve. 
# Alice finds that, with the optimal strategy for her game, the expected 
# number of turns taken until she wins is approximately 5. 673651. Assuming 
# that Bob plays with an optimal strategy, what is the expected number of 
# turns taken until he wins? Give your answer rounded to 6 places after the 
# decimal point.
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 640
    timed.caller(dummy, n, i, prob_id)
# Solution of; # Project Euler Problem 640: Shut the Box # https://projecteuler.net/problem=640 # # Bob plays a single-player game of chance using two standard 6-sided dice and # twelve cards numbered 1 to 12. When the game starts, all cards are placed # face up on a table. Each turn, Bob rolls both dice, getting numbers $x$ and # $y$ respectively, each in the range 1,. . . ,6. He must choose amongst three # options: turn over card $x$, card $y$, or card $x+y$. (If the chosen card is # already face down, it is turned to face up, and vice versa. )If Bob manages # to have all twelve cards face down at the same time, he wins. Alice plays a # similar game, except that instead of dice she uses two fair coins, counting # heads as 2 and tails as 1, and that she uses four cards instead of twelve. # Alice finds that, with the optimal strategy for her game, the expected # number of turns taken until she wins is approximately 5. 673651. Assuming # that Bob plays with an optimal strategy, what is the expected number of # turns taken until he wins? Give your answer rounded to 6 places after the # decimal point. # # by lcsm29 http://github.com/lcsm29/project-euler