Sunday Times Teaser 2747 (2015-05-17)

marbles.sh

#!/bin/bash

for sum in {399..350..-1}; do
	for red in {4..200}; do
		blue=$((sum-red))

		num1=$red
		den1=$((blue+red))

		num2=$((red-1))
		den2=$((blue+red-1))

		num3=$((red-2))
		den3=$((blue+red-2))

		num4=$((red-3))
		den4=$((blue+red-3))

		echo "$red Red + $blue Blue = $sum"
		echo "($den1*$den2*$den3*$den4)/($num1*$num2*$num3*$num4)" | bc -l
	done
done | grep -B1 "\<[0-9]\{4\}\.000000"

marbles.txt

nearly 400 marbles
some red, rest blue

400 > (red+blue) > 350

red < blue

select 4 marbles
probability of all four being red is 1/X
where X is a 4 digit integer

How many red  marbles?
How many blue marbles?