Where is the castle?

Logic Level 2

There is an island named Graff where knights and knaves live.
Knights always speak the truth; knaves always speak lies.
You ask 4 people (at the same location) where the castle is, and they reply:

Alex: "The castle is North of here. Jim is a knave."
Jeff: "The castle is West of here. Jim is a knight."
Jim: "The castle is East of here. Jeff is a knight."
Alice: "The castle is South of here. Alex is a knave."

In which direction is the castle?

North West South East There is not enough information

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.

3 solutions

Tarmo Taipale
Jun 11, 2016

Relevant wiki: Truth-Tellers and Liars

Alex says "Dont listen to Jim" (states that Jim never speaks the truth). Jeff says "Listen to Jim" (states that Jim always tell the truth). These statements are contrary to each other, so either of them must be true.

If Jim was the knight (always honest), Jeff would also tell something true. However, there is only one knight, and the others are knaves ( who always lie ), so Jeff and Jim can't both tell the truth, so Jeff's statement (Jim is honest) is false.

This means Alex must have told the truth, and because he is the knight (and always tells the truth) his first statement is true, and the castle is in the north.

How do you deduce that there is only one knight?

Pamela Davis - 4 years, 11 months ago

Log in to reply

Well, I forgot to say that, but the first statements of each person are contrary to each other, so only one person can be telling truth.

Tarmo Taipale - 4 years, 11 months ago

Log in to reply

One of those A-HA moments! Thanks!

Pamela Davis - 4 years, 11 months ago

How do you conclude that Alice didn't tell the truth?

Ardy Lay - 4 years, 11 months ago
Adarsh Mahor
Jul 29, 2016

Just assume any one of them is knight and follow and then again for rechecking assume another ad knight till we can sure

Thank you for this!

Diana Bradish - 1 year, 2 months ago
Dario Giandinoto
Jun 11, 2016

Since all four people give different statements on the first answer, we must decide their truthfulness based on their second answer. Jim says to listen to Jeff, who in the first statement gave a different answer than him, so he was lying at least in one of his two statements, but since Knaves always lie and Knights never lie, it means that he lied on both statements. Same goes for Jeff. Since we know that Jim and Jeff are Knaves, and since Alex says not to listen to Jim, he's truthful; while Alice says not to listen to Alex, therefore to listen to Jim, who is a Knave. So the only one speaking the truth is Alex, and the right answer is North.

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...