1 ! Copyright (c) 2008 Eric Mertens.
2 ! See https://factorcode.org/license.txt for BSD license.
3 USING: kernel math math.functions project-euler.common ;
6 ! https://projecteuler.net/index.php?section=problems&id=100
8 ! DESCRIPTION ! -----------
10 ! If a box contains twenty-one colored discs, composed of fifteen blue discs
11 ! and six red discs, and two discs were taken at random, it can be seen that
12 ! the probability of taking two blue discs, P(BB) = (15/21)*(14/20) = 1/2.
14 ! The next such arrangement, for which there is exactly 50% chance of taking
15 ! two blue discs at random, is a box containing eighty-five blue discs and
16 ! thirty-five red discs.
18 ! By finding the first arrangement to contain over 10^12 = 1,000,000,000,000
19 ! discs in total, determine the number of blue discs that the box would contain.
25 : euler100 ( -- answer )
27 [ dup dup 1 - * 2 * 10 24 ^ <= ]
28 [ [ 6 * swap - 2 - ] keep swap ] while nip ;
30 ! TODO: solution needs generalization
32 ! [ euler100 ] 100 ave-time
33 ! 0 ms ave run time - 0.14 SD (100 trials)