Enigma 352: In the bag
From New Scientist #1501, 27th March 1986 [link]
Yesterday, I was presented with an unusual box containing 13 painted Easter eggs. Each egg was either red, white or blue and there was at least one egg of each colour. If I had been in a dark room, the minimum number of eggs I would have had to withdraw from the box to be certain of picking at least three eggs of the same colour was the same as the number of blue eggs in the box.
Being superstitious, I decided against leaving 13 eggs in the box and transferred a number to a black bag. This bag may not have been empty before I added the coloured eggs. If it wasn’t, then it contained one or more black eggs and nothing else. However, two things are certain. One is that if I were in a dark room, the minimum number of eggs I would now have to withdraw from the box to be sure of having at least three eggs of the same colour is the same as the number of blue eggs in the bag. The second is that the chances of picking out a white egg from the bag with one attempt are the same as the chances of picking out a white egg from the box with one attempt.
But I am in a dark room. Trying to deduce the contents of that black back without turning the light on and looking is keeping me awake late into the night.
How many red, white, blue and black (if any) eggs are there in the bag?