# A Puzzle about Labeled Logicians

A Puzzle about Labeled Logicians

This Demonstration generates a puzzle about logicians who derive conclusions from given assumptions and previous statements.

There are logicians in a room, all wearing jackets with on the front as labels. On the back of at least one of the jackets is a big letter X. This fact is known to all. Each of the logicians can see everyone else's back, but not their own. The problem for each of them is to figure out whether they have an X or not.

n

1,2,3,…,n

They do this in the course of several rounds. In each round, the logicians who have not yet decided if they have an X on their back speak in order of their labels. Each logician says one of the following statements:

A: "I don't know whether I have an X on my back."

B: "I don't have an X on my back."

C: "I do have an X on my back, and at least one other logician does also, but has not said so yet."

D: "I do have an X on my back, and all other logicians who do have already said so."

A logician takes part in the next round only if he or she makes statement A. Of course, they are perfect logicians and never lie.