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.)
Congrats, Charlie! Beat me to it again. I used essentially the same evaluation/calculation of probability formula, on a slightly different range of number of colours and number of each colour. In haste I wrote "19 piles of 10 different colors" when I was actually testing the set of 10 each of 19 different colours.
I noticed that all of the nearest results (probabilities off the least) used piles of 10 each. I tested for up to 100 piles but found no other solutions. Execution time 0.04 seconds.
Agreed
