Grades 11-12 Video Solutions 2013-Levels 11&12 Video Solutions 2013 problem28

Video Transcription

Question number 28. On the island of knights and knaves, there live only two types of people. Knights who always speak the truth and knaves who always lie.  I met two men who lived there and asked the taller man if they were both knights. He replied but I could not figure out what they were.  So I asked the shorter man if the taller was a knight. He replied and after that I knew which type they were. Were the men knights or knaves?  The key to solving such a problem is to look for a paradox because a paradox is a mathematical statement that is both true and false.  So in particular, a knight who is supposed to only speak the truth cannot speak in paradoxes. So after speaking to the tall man, the answer is not clear.  So we know that the tall man spoke a paradox. And we conclude that he is not a knight because knights do not speak in paradoxes.  And we also conclude that both of the men cannot be knights as one of them is already for sure not a knight. Now after listening to the shorter man we know what the answer is  because the question posed to him is is the taller man a knight which we already know to be false? And now we just have to decide is the shorter man a knave or a knight?  And since after listening to his answer we can decide which one it is, he must have answered no. So he must have confirmed what we already knew.  So he spoke the truth and we know that he must have been a knight. So the answer here is D.

Video Summary

On the island of knights and knaves, knights always tell the truth while knaves always lie. When questioned, the taller man's response was unclear, suggesting he spoke a paradox, indicating he is a knave. Since the taller man cannot be a knight, both cannot be knights. The shorter man was asked if the taller man was a knight. With the taller man's status known as false, the shorter man's truthful response, confirming this information, means he is a knight. Therefore, the taller man is a knave, and the shorter man is a knight.