Puzzle: Certainty amid Uncertainty

In a recent Michael Mauboussin talk that I linked to here, he raises an interesting puzzle, which may be paraphrased as:

"Person A (male), who is married, is looking at person B (female). In turn, person B is looking at person C (male), who is unmarried.  Is a married person looking at an unmarried person?"

There is uncertainty in the set up. We don't know if person B is married or not. If we knew, then the question would be trivial.

However, the question being asked of us, does not require complete information. In fact, we can answer the question, with certainty, without knowing the marital status of person B.

The answer is yes, there is a married person looking at an unmarried person.

We recognize that person B is either married or unmarried.

• if she is married, then she is looking at person C, who is unmarried.
• if she is unmarried, then person A, who is married, is looking at her.

In either case, there is someone who is married looking at someone who is not!