Being a Knight Deterimes Everything, or Does It?
On the island of knights, knaves, and jokers, where knights always tell the truth, knaves always lie, and jokers can do either, you meet three islanders: Alex, Miranda, and Joe. Each say as the follows:
Alex: "I am a knight."
Miranda: "One of us is a knight, another is a knave, and the last of us is a joker."
Joe: "Miranda is a knave."
Is Miranda a knight, knave, or a joker?
HINT: Look at all possible scenarios before making your conclusion.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
There is more than one way to solve this. In fact, Miranda could be a knight, knave, or a joker! Here's why:
Suppose Miranda is a Knight: If Miranda is a knight, then Alex is a knave and Joe is a Joker, or vice versa. If you use this, you will find that this scenario does work, so it is a possiblility. It is unnecessary to state the solution (if any) for Alex being a Joker and Joe being a knave because we have already found a solution that works, although you can try to find one on your own!
Suppose Miranda is a Knave: If Miranda is a knave, then Alex is a knight, knave, or joker, and so is Joe. If Alex is a knave, then this solution works, because this would mean that there must be at least one other knave. As you may notice, if Alex and Miranda are both knaves, then Joe could be a knight or a joker.
Suppose Miranda is a Joker: If Miranda is a joker that is telling the truth, then Alex being a knight, and Joe being a knave solves this scenario.
Therefore, Miranda could be a knight, knave, or a joker.