An urn contains a number of colored balls, with equal numbers of each color. Adding 20 balls of a new color to the urn would not change the probability of drawing (without replacement) two balls of the same color.
How many balls are in the urn? (Before the extra balls are added.)
Trying combinations up to 50 piles of up to 90 each as a start, and allowing for computer rounding issues, the only set that seems within tolerances is for an original configuration of 19 piles of 10 different colors (total 190). Adding 20 would make a total of 210. Both of these give a probability of 0.0476190 that the second draw would match the color of the first draw. After posting I'll look at Charlie's post to see if we agree, and if so if I just tried to few combinations.
Computer Search
