On page 30 of Raymond Smullyan's book To Mock a Mockingbird, we are told that there are four brothers, indistinguishable in appearance, of which
- Arthur is an accurate truth-teller,
- Bernard is an inaccurate truth-teller,
- Charles is an accurate liar,
- David is an inaccurate liar,
where "inaccurate" means that one always believes that true proposition are false and vice versa.
In the puzzle 2 at page 30, the premise is
- Arthur is married and wealthy,
- Bernard is married and not wealthy,
- Charles is not married and wealthy,
- David is not married and not wealthy.
Upon meeting one of the four brothers, what three-word question is enough to find out whether he's married?
The author gives this solution, which makes use of the property of being wealthy:
Are you wealthy?
However, since the property of being wealthy is owned only by those two brothers which are accurate (though one is truth-teller and one is liar), isn't the following question, which doesn't rely on the property of being wealthy, enough?
Are you accurate?