WOLFRAM|DEMONSTRATIONS PROJECT

A Puzzle about Labeled Logicians

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number of logicians
13
number of logicians with X
5
last entry to table
A
B
C
D
show
blank table
solution table
new puzzle
There are 13 logicians, all with labels on their front.
Some have an X on their back, as well.
This is the set of labels of the logicians with an X on their back:{1,4,6,7,12}.
Fill in the table with their statements!
If a logician does not take part in a round, leave that space empty.
1
2
3
4
5
6
7
8
9
10
11
12
13
1
2
3
4
5
6
7
What is the last entry to the table?
This Demonstration generates a puzzle about logicians who derive conclusions from given assumptions and previous statements.
There are
n
logicians in a room, all wearing jackets with
1,2,3,…,n
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.
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.