# Solution of;
# Project Euler Problem 285: Pythagorean odds
# https://projecteuler.net/problem=285
# 
# Albert chooses a positive integer k, then two real numbers a, b are randomly 
# chosen in the interval [0,1] with uniform distribution. The square root of 
# the sum (k·a+1)2 + (k·b+1)2 is then computed and rounded to the nearest 
# integer. If the result is equal to k, he scores k points; otherwise he 
# scores nothing. For example, if k = 6, a = 0. 2 and b = 0. 85, then (k·a+1)2 
# + (k·b+1)2 = 42. 05. The square root of 42. 05 is 6. 484. . . and when 
# rounded to the nearest integer, it becomes 6. This is equal to k, so he 
# scores 6 points. It can be shown that if he plays 10 turns with k = 1, k = 
# 2, . . . , k = 10, the expected value of his total score, rounded to five 
# decimal places, is 10. 20914. If he plays 105 turns with k = 1, k = 2, k = 
# 3, . . . , k = 105, what is the expected value of his total score, rounded 
# to five decimal places?
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 285
    timed.caller(dummy, n, i, prob_id)
