Logic
# Truth-Tellers and Liars

A cookie went missing from Emily's cookie jar, and she knows exactly one of Amir or Jake ate it.

Both Amir and Jake said "I did not eat the cookie".

Emily knows that Amir always lies and Jake always tells the truth. Can she figure out who ate her cookie? If so, who is the culprit?

During a laboratory project, exactly one of Jesse, Walter, or Skyler broke a glass flask. When questioned by the teacher, their responses were as follows:

**Jesse**: Walter broke it.

**Walter**: Skyler broke it.

**Skyler**: Walter broke it.

Because all 3 students were sweating and panicking, the teacher knew that all of them were lying. Can the teacher deduce who broke the flask? If yes, who broke it?

In an island, there are two types of people: *knights*, who only speak truths; and *knaves*, who only speak lies. Bruce, Thomas, and Martha are friends who live on the island. One day, the following conversation occurs:

Thomas: Bruce is a knight.

Martha: Bruce is a knave.

Can we determine whether Bruce is a knight or a knave? If yes, what type of person is Bruce?

A father gave each of his three daughters 5 or 7 cookies each. The daughter(s) who received 5 cookies always lie, while the daughter(s) who received 7 cookies always tell the truth.

When asked about the number of cookies they received, they responded as follows:

**Danielle**: We have a total of 15 cookies.

**Erica**: We have a total of 17 cookies.

**Fiona**: We have a total of 19 cookies.

Knowing that at least one of the 3 daughters spoke the truth, what is the total number of cookies that the daughters received?

Huey, Dewey, and Louie were involved in stealing a cookie from their uncle, Donald. When confronted, the three brothers made the following claims:

Huey said: I stole the cookie.

Dewey said: Huey stole the cookie.

Louie said: Dewey stole the cookie.

Donald knows that all three of them are lying. If exactly one of them stole the cookie, who did it?