### Some Logic Problems

The following problems are adapted from a book of Logic Problems by Raymond Smullyan: The Lady or the Tiger? and Other Logic Puzzles, Times Books, 1982. Last updated 02/02/97

Solution of these problems does involve applications of the rules of propositional logic (plus some translations from words to symbols). Enjoy!
You should feel free to pose questions about these on the math2090 list. However, good netiquette says that if you are posting an (attempted) solution, your subject header should start with Spoiler, so other people can choose to ignore this until they are finished.

If you have other interesting Logic Puzzles to propose, submit them to either instructor or the tutors.

### Danger or Freedom

The first series of problems involve a mythical kingdom in which prisoners are taken into a room and, after some hints, given a choice of doors to open. Each door may lead to freedom or it may lead to danger (a tiger who will kill them). Each door has a sign on it with a sentence.

## Second Day

The king decided to make the puzzles more difficult. If the first door leads to freedom, then the sign on that door is true; if the first door leads to danger, then the sign on that door is false.
For the second door, this is reversed: if the second door leads to freedom, the sign on the second door is false; if the second door leads to danger, the sign on the second door is true.

### Fourth Problem

• The sign on the first door reads:
Both doors lead to freedom.
• The sign on the second door reads:
Both doors lead to freedom.
Now which door do you choose?

## First Day

### Third Problem

In the third trial, you are told that, again, either both signs are true or both signs are false. There are still two doors:
• The sign on the first door is:
Either this door leads to danger or the other door leads to freedom.
• The sign on the second door is:
The other door leads to freedom.

### Second Problem

In the second trial, there are two doors:
• The sign on the first door is:
At least one of these doors leads to freedom.
• The sign on the second door is:
The other door leads to danger.
You are given one further hint
Either both signs are true or both signs are false!

Which door should you choose?

### First Problem

In the first situation, there are two doors:
• The sign on the first door is:
This door leads to freedom and the other door leads to danger.
• The sign on the second door is:
One door leads to freedom and the other door leads to danger.
You are given one further hint
One sign is true and the other is false!

Which door should you choose?