! Copyright (c) 2008 Eric Mertens.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel math math.functions sequences ;
IN: project-euler.100

! http://projecteuler.net/index.php?section=problems&id=100

! DESCRIPTION
! -----------

! If a box contains twenty-one coloured discs, composed of fifteen blue discs
! and six red discs, and two discs were taken at random, it can be seen that
! the probability of taking two blue discs, P(BB) = (15/21)*(14/20) = 1/2.

! The next such arrangement, for which there is exactly 50% chance of taking
! two blue discs at random, is a box containing eighty-five blue discs and
! thirty-five red discs.

! By finding the first arrangement to contain over 10^12 = 1,000,000,000,000
! discs in total, determine the number of blue discs that the box would contain.


! SOLUTION
! --------

: euler100 ( -- answer )
    1 1
    [ dup dup 1- * 2 * 10 24 ^ <= ]
    [ tuck 6 * swap - 2 - ] while nip ;

! TODO: solution needs generalization

! [ euler100 ] 100 ave-time
! 0 ms ave run time - 0.14 SD (100 trials)

MAIN: euler100