Languages of Logic

Knights, Knaves, and Logic

This is the second of Brilliant's courses dedicated solely to logic. If you've never solved a knights and knaves puzzle before, you might want to start with our first logic course, which introduces knights and knaves puzzles and many other logic puzzle types.

Alternatively, if you already have a good grasp of how "and", "or", "not", and "if...then" statements are used in logic puzzles, then you could also be fine jumping in right here! Be warned though: the puzzles get very intense at the end of this sequence!

Knights, Knaves, and Logic

Introduction

           

Knights, Knaves, and Logic

On a certain island, there are only two types of islanders:

knights, who always tell the truth, and
knaves, who always lie.

You meet two islanders named Aditya and Bowie.

What types of islanders are Aditya and Bowie?

Details:

  • All islanders know their own type and the names and types of everyone else on the island.
  • "Or" is always intended in the inclusive sense; that is, the statement "X or Y" is true in the case where only X is true, in the case where only Y is true, and in the case where both X and Y are true.

Knights, Knaves, and Logic

Introduction

           

Knights, Knaves, and Logic

On the same island, you find three friends named Channing, Daija, and Eira.

What type (knight or knave) is Channing?

Knights, Knaves, and Logic

Introduction

           

Knights, Knaves, and Logic

The next problem involves an "if...then" statement. If you've done our Logic course, you may remember the text below; this is just a reminder.


Consider the claim “If it’s raining on me, then I use my umbrella to keep dry." The only condition that makes the claim false is if it's raining and the umbrella is not being used. (Intuitively, one can't claim a person is lying about using umbrellas when it rains if it isn't raining yet!)

In logic, a statement of the form, “If A, then B” is false only in the case where A is true and B is false. Otherwise, the statement is true.

Knights, Knaves, and Logic

Introduction

           

Knights, Knaves, and Logic

You come across two more friends named Fiadh and Greg, but only Fiadh says anything:

Fiadh says, "If I am a knight, Greg is a knave."

What type is Greg?

Knights, Knaves, and Logic

Introduction

           

Knights, Knaves, and Logic

Finally, just as you are about to leave the island, you find a group of four islanders named Kade, Lovelace, Maxwell, and Nelly, and again you ask what types they are.

Given you know that at least one of them is a knave, exactly how many are knaves?

(Remember, we're still using "or" inclusively, so when the statement is used, it could refer to either one or both!)

Knights, Knaves, and Logic

Introduction

           
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