37 lines
1.1 KiB
Factor
37 lines
1.1 KiB
Factor
! 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
|