Knights And Knaves 1

Logic Level 1

On an island live knights and knaves. Knights always tell the truth and Knaves always lie. One day, Bob came across five islanders. What they said were as follows:

  • Alice: Boris is a knave.
  • Boris: Alice and Dan are knaves.
  • Charles: At least two of us are knaves.
  • Dan: Charles is a knave.
  • Edward: There are exactly 3 knights.

What is Charles?

Knave Knight Not Enough Info to tell

Yuhan Zhai by yuhan zhai , 28, United Kingdom

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5 solutions

Winston Choo
Jan 11, 2020

From Alice's statement, Alice and Boris can't be both Knights or both Knaves, so there must be 1 Knight and 1 Knave between them.

Same goes for Charles and Dan, there must be 1 Knight and 1 Knave between them from Dan's statement.

There are at least 2 Knights and 2 Knaves, so Charles' statement must be True.

Therefore Charles is a Knight.

Nothing can be said about Alice, Boris and Edward as there is not enough information to tell.

3 Helpful 1 Interesting 2 Brilliant 0 Confused
Richard Desper
Jan 15, 2020

If Charles is a knave, the falsity of his statement implies that he's the only knave. This cannot be reconciled with Alice's statement. Either it's true, in which case Boris is a knave, or it's false, in which case Alice is a knave.

Charles must be a knight.

1 Helpful 1 Interesting 1 Brilliant 0 Confused
Saya Suka
Jan 12, 2020

A and B is accusing each other, so one of them must be a knave. Now look at C's statement, the only way it's going to be wrong --> he's lying --> knave is if all three of the rest, CDE are Knights, which is impossible since he can't be both a knave and a knight simultaneously. So C is knight and D is knave.

1 Helpful 1 Interesting 1 Brilliant 0 Confused

Edward can be whatever he wants.

Saya Suka - 4 months ago
Chris Lewis
Jan 12, 2020

By Alice and Boris' statements, at least one of Alice and Boris is a knave. So if Charles were a knave, his statement would be true; contradiction. So Charles must be a knight .

Using upper case initials to denote knights, and lower case to denote knaves, valid solutions are AbCde, AbCdE, aBCde, aBCdE.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

From the given statements it is clear that Boris, Charles and Edward are knights and Alice and Dan are knaves.

1 Helpful 1 Interesting 1 Brilliant 3 Confused

Can you prove that this is the only solution?

Pi Han Goh - 1 year, 5 months ago

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There are several possible solutions, though Charles is always a knight and Dan always a knave.

If there are two knights and two knaves among Alice, Boris, Charles and Dan, then Edward can either be a knight (in which case, there are three knights, and his statement is true), or a knave (in which case his statement is false, and everything is still consistent).

Chris Lewis - 1 year, 5 months ago

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