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Truth-Tellers and Liars

Time to play detective! Every puzzle in this collection contains a set of statements, but it's up to you to figure out which of those statements are true and which of them are false. See more

Warmup

         

Suppose you are visiting an island with knights, who always tell the truth, and knaves, who always lie.

Which statement is \( \color{red} { \text{impossible} } \) for an islander to make?

Suppose you are in a dungeon with two doors. One of the doors has a treasure and the other has a terrible monster.

The doors have signs on them. You know the sign on a door either tells the truth or lies.

FIRST DOOR: "Both doors are lying."

SECOND DOOR: "The treasure is in this room."

Where is the treasure?

\[\begin{array}{|l|} \hline {\text{ The next sentence is true. }} \\ {\text{ The previous sentence is false. }} \\ \hline \end{array} \]

Is the first sentence true?

Suppose you are visiting an island with sknights and sknaves.

Sknights tell the truth on every day but Saturday, on which they always lie.

Sknaves lie on every day but Saturday, on which they always tell the truth.

You don't know what day of the week it is. You meet an islander and ask, "Is it Saturday?" They respond "Yes."

What type must the islander be?

Suppose you are visiting an island with knights, who always tell the truth, and knaves, who always lie.

You ask an islander a question. Which question has a \( \color{red} { \text{guaranteed} } \) answer of "no"?

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