Result of Challenge 27
After a long challenge run, here is the solution to Zeno's Challenge #27! Scores of submissions were received from around the globe, with many mixed solutions and varied reasoning strategies! The orginal challenge is repeated, with the solution below. Cheers!
Charles' Three Customers
One late night at Zeno's, our friend Charles (who is a cat lover) encountered three new patrons at the coffeehouse, who didn't identify themselves as the Knight, the Knave or the Shortcomer, but assured him and others that they were, in fact, all three, exactly one each. The Knight, all are to assume, always tells the truth, whilst the Knave always lies. The Shortcomer sometimes tells the truth and sometimes lies. They made the following statements to Charles:
A. I love cats;
B. C always tells the truth;
C. A hates cats.
Charles was asked to bet $100 that he could not correctly identify which one of these patrons is the Knight. Should he take the bet? From this information, which statement is most likely that made by the Knight?
For the chart below, assume A=knave, I=knight, and S=shortcomer....(think of this like a truth-table)
A B C
1.A I S
2.A S I
3.I A S
4.I S A
5.S A I
6.S I A
Conditions 1, 5 and 6 cannot occur because of contradictory results. In two of possibilities 2, 3 and 4, the knight is A, the person who claims to love cats. So Charles would be wisest to bet on A, as there is better than a 66% chance that that individual is the knight!!
Mark Hartswood's (Edinburgh) solution looks like this:
comments: Charles might consider taking the bet - he has a 2/3 chance
A is most likely to be the knight.
There are 6 possible ways of assigning the Knave, the Knight
and the Shortcomer to A B and C, however...
The Knight is not B - because the Knight always tells the
truth and wouldn't therefore imply that either the Shortcomer or the Knave was the Knight. This eliminates
the two of the possible solutions (ie those with the Knight
as B and the Knave and Shortcomer as either A or C).
The solution where the Knave is B and the Knight is C can
also be eliminated - because the Knave would be telling the
Three possible solutions remain, ie:
A-Knight B-Knave C-Shortcomer
A-Knight B-Shortcomer C-Knave
A-Knave B-Shortcomer C-Knight
Giving a 2/3 probability that the Knight is A.
Thank you and good Knight,
Good night to you, Mark!:)