I have a lot of meeples, which for reasons of my own I keep in a set of labelled jars. I have a jar of red meeples, a jar of green meeples, and a jar of red and green meeples that I have yet to sort out. In all three jars there are a lot of meeples, and the meeples in the unsorted jar are not necessarily split evenly between the two colours, but I do know the unsorted jar contains some meeples of both colours.
Now, somewhat mischievously and for equally opaque reasons, a friend of mine has played a trick on me. He has put the contents of each jar wholly in a different jar, so that none of the labels now match the contents. Curse him! Curse him to Carcassonne and back! Curse him and the small purple dragon he rode in on!
Anyway, my impish friend has a challenge for me: He wants me to figure out the contents of each jar. I can’t look into the jars (that would be too easy) or pick them up or weigh them or anything like that, but I may take meeples out of the jars, one at a time, and look at them.
What is the minimum number of meeples I have to look at to be certain that I know which jar is which?
And once you can answer that, what is the answer to the same question if I have a set of four labelled jars — a red jar, a green jar, a yellow jar, and an unsorted jar containing some mixture of red, green and yellow meeples — the contents of which have been similarly interchanged so that none of the labels match?
Update: Do feel free to leave a comment and let me know your answers!