0910.2: Solution

In our last puzzle, you were asked to identify three couples at the Colgate-Hamilton mixer: a Colgate couple, a Hamilton couple, and a mixed pair.  Each couple held a sign mis-describing themselves.  Our challenge was to find the fewest number of questions in which you can determine which sign correctly describes which couple.

The solution may be discovered by using merely one question.  Since each couple held the wrong sign, we can be sure that the couple holding the Hamilton-Colgate sign (call them couple A) is either the Colgate pair or the Hamilton pair.  Asking one member of that pair tells us which.  Trade signs between couple A and whichever of the remaining two couples is mistakenly holding couple A’s correct sign.  Now, couple A is correctly identified, but one couple is still holding their original sign.  Trade signs between the two remaining couples, and each couple will be correctly identified.