BrettSpiel is a blog about board game design, written by game designer Brett J. Gilbert.

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The Puzzling Meeple: Jar Jar Jinx

The Puzzling Meeple: Jar Jar Jinx

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!

1) you only need to look at one from the mixed and you're done, for obvious reasons
2) look at one from the mixed, then look at one from the color you found in the mixed and you're done

You only need to look at one from the jar labeled as mixed. That tells you everything you need to know. (Are we supposed to comment the answer?)

Scurra said...

April 04, 2011 2:36 pm

I think you still need to take a third in the four jars example to be sure. There are plenty of combinations that would work with only taking 2, but the existence of even one possibility that requires 3 means that you have to take 3 in those circumstances.

(e.g. you take a Red from the "Mixed" jar - so it must contain Red. You then take a Green from the "Red" jar. Does the "Red" jar contain Green or Mixed?
And if you switch to a different Jar for the 2nd pick, the same possibility exists.)

It seems like the minimum draw in the four jar case is indeterminate: you'd presumably draw first from the mixed jar, then alternate draws from the other jars until you drew another of the same color as the first. It's possible to do that in two draws, but it's not the case that the solution always appears after two draws. I probably haven't thought it through very well, though.

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