Logic

Truth-Tellers and Liars

Truth Tellers and Liars: Level 2 Challenges

           

Only one of three people, Alice, Beto, and Carl stole the money from Ms. Doubtfire. She hires you as a consultant detective. After interrogating them each, you have the following:

Alice\textbf{Alice}: Don't trust Carl. He is lying and he took the money.

Carl\textbf{Carl}: Beto is lying but Alice didn't take the money.

Beto\textbf{Beto}: Carl took the money. I didn't take the money.

After gathering information, you know that whenever one of them lies, they lied for both parts of their statement. Also, if one of them tells the truth, they tell the truth for both parts of their statement. Who took the money?


Remark: I'm giving credit to my logic course from this website brilliant.org. I got some ideas from there.

John tells the truth on Mondays, Thursdays, and Saturdays, but lies on all the other days of the week.

One day he said, “I will tell the truth tomorrow.”

On which day of the week did he make this statement?

Only one of the following statements is true. Which one?

1) Statement 2 is true.
2) Statement 5 is false.
3) All five statements are true.
4) All five statements are false.
5) Statement 1 is false.

Knights always tell the truth and Knaves always lie.

In a group of six people, the following statements are made:

  • Alice says, "None of us are Knights."
  • Bob says, "Exactly two of us are Knights."
  • Cathy says, "At least three of us are Knights."
  • Dave says, "At most three of us are Knights."
  • Evelyn says, "Exactly five of us are Knights."
  • Frank says, "Exactly one of us is a Knight."

How many Knights are there?

An island has only two types of people: Knights (who always speak the truth) and Knaves (who always lie).

I met two men who lived there and asked the taller man "Are both of you Knights?".
He replied with a "Yes" or "No", but from his answer, I could not figure out what type of person each man was.
I then asked the shorter man "Is the taller man a Knight?".
He replied with a "Yes" or "No", and after that I knew which type of person each man was.

Were the men Knights or Knaves?

On one side of the card it is written that
"The statement on the other side of this card is true"

And on the other side it is written that
"The statement on the other side of this card is false"

Which statements is/are true?

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