Hi all,
I have been doing for fun this problem in projecteuler.net. The problem is as follows:
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Peter has nine four-sided (pyramidal) dice, each with faces numbered 1, 2, 3, 4.
Colin has six six-sided (cubic) dice, each with faces numbered 1, 2, 3, 4, 5, 6.
Peter and Colin roll their dice and compare totals: the highest total wins. The result is a draw if the totals are equal.
What is the probability that Pyramidal Pete beats Cubic Colin? Give your answer rounded to seven decimal places in the form 0.abcdefg
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#!/usr/bin/python
from datetime import datetime
from decimal import *
def getProb49():
probabilities=[0]*(4*9+1)
for d1 in range(1,5):
for d2 in range(1,5):
for d3 in range(1,5):
for d4 in range(1,5):
for d5 in range(1,5):
for d6 in range(1,5):
for d7 in range(1,5):
for d8 in range(1,5):
for d9 in range(1,5):
probabilities[d1+d2+d3+d4+d5+d6+d7+d8+d9] += 1
return probabilities
def getProb66():
probabilities=[0]*(6*6+1)
for d1 in range(1,7):
for d2 in range(1,7):
for d3 in range(1,7):
for d4 in range(1,7):
for d5 in range(1,7):
for d6 in range(1,7):
probabilities[d1+d2+d3+d4+d5+d6] += 1
return probabilities
def main():
stime=datetime.now()
prob66 = getProb66()
prob49 = getProb49()
"""
sumprob = 0
index = 0
for prob in prob49:
print index, float(prob)/4**9, prob
sumprob += prob
index += 1
print sumprob,4**9
"""
# Probability for prob49 > prob66
tot49 = 4**9
tot66 = 6**6
getcontext().prec = 7
sol = 0
index = 0
for prob in prob49:
sol += prob * sum(prob66[0:index-1])
print index, Decimal(prob)/Decimal(tot49), Decimal(sum(prob66[0:index-1]))/Decimal(tot66),float(sol)/(tot49*tot66),sol
index += 1
print Decimal(sol)/Decimal(tot66*tot49)
print datetime.now()-stime
if __name__ == "__main__":
main()What I basically do is calculating all the possibilities for obtaining 0,1,..,36 with the dices and write it in a list.
Then I iterate over the two lists and I try to sum all the cases where the 4 side dice win
My problem is that even it runs pretty fast I don't get the right solution.
I know that when index=0 the prob66[0:-1] does not works as I expected but since it is multiplied by 0 in that point is not the problem, (though is not a really good coded)
I can't figure out what is wrong
Thank you!
