# Logic Puzzles

### Knaves and Knights

An island is inhabited by two classes of people: *knights*, who make only true statements, and *knaves*, who make only false statements. Three inhabitants are conversing. Alfred says, “All of us are knaves.” Bert says, “Exactly one of us is a knight.” What are Alfred, Bert, and Charles?

### Fork in the Road

The Clinton Brothers (Bill and Ben) are identical twins. Ben is known to be totally truthful, and the other is a politician. You meet one of them at a fork in the road, and there’s no sign to indicate which is the road to Washington (your destination). What single question can you ask the brother who is there, to discover the correct road? Assume that you don’t know if it’s Bill or Ben, and that politicians always lie…

### The Portrait

Looking at a portrait, a man said “Brothers and sisters have I none, but that man’s father is my father’s son.” Whose portrait is it?

### False Statements

Which of the following statements is true?

- Exactly one of these ten statements is false.
- Exactly two of these ten statements are false.
- Exactly three of these ten statements are false.
- Exactly four of these ten statements are false.
- Exactly five of these ten statements are false.
- Exactly six of these ten statements are false.
- Exactly seven of these ten statements are false.
- Exactly eight of these ten statements are false.
- Exactly nine of these ten statements are false.
- Exactly ten of these ten statements are false.

What happens if you remove the word ‘Exactly’ from all the statements?

### $29

Three people check into a hotel. They pay $30 to the manager and go to their room. The manager finds out that the room rate is $25 and gives $5 to the bellboy to return. On the way to the room the bellboy reasons that $5 would be difficult to share among three people so he pockets $2 and gives $1 to each person.

Now each person paid $10 and got back $1. So they paid $9 each, totalling $27. The bellboy has $2, totalling $29.

Where is the remaining dollar?

- Bookworm
- A bookworm eats from the first page of an encyclopedia to the last page. The bookworm eats in a straight line. The encyclopedia consists of ten 1000-page volumes and is sitting on a bookshelf in the usual order. Not counting covers, title pages, etc., how many pages does the bookworm eat through?Answer
- Which Box Contains the Gold?
- Two boxes are labeled “A” and “B”. A sign on box A says “The sign on box B is true and the gold is in box A”. A sign on box B says “The sign on box A is false and the gold is in box A”. Assuming there is gold in one of the boxes, which box contains the gold?Answer
- Camel Race
- An Arab sheikh tells his two sons to race their camels to a distant city to see who will inherit his fortune. The one whose camel is slower will win. The brothers, after wandering aimlessly for days, ask a wise man for advise. After hearing the advice they jump on the camels and race as fast as they can to the city. What does the wise man say?Answer
- Centrifuge
- You are a biochemist, working with a 12-slot centrifuge. This is a machine that has 12 equally spaced slots around a central axis, in which you can place tubes containing chemical samples you want separated. When the machine is turned on, the samples whirl around the central axis and the denser substances are forced to the bottom of the tubes.To ensure that the samples are well separated, they must be distributed in the 12 slots such that the centrifuge is balanced evenly. For example, if you wanted to centrifuge 4 samples, you could place them in slots 12, 3, 6 and 9 (assuming the slots are numbered from 1 to 12 like a clock).Problem: Can you use the centrifuge to separate 5 samples?Answer
- Elimination
- 97 baseball teams participate in an annual state tournament. The way the champion is chosen for this tournament is by the same old elimination schedule. That is, the 97 teams are to be divided into pairs, and the two teams of each pair play against each other. After a team is eliminated from each pair, the winners would be again divided into pairs, etc. How many games must be played to determine a champion?Answer
- Flowers
- How many flowers do I have if all of them are roses except two, all of them are tulips except two, and all of them are daisies except two?Answer
- Locks and Boxes
- You want to send a valuable object to a friend. You have a box which is more than large enough to contain the object. You have several locks with keys. The box has a locking ring which is more than large enough to have a lock attached. But your friend does not have the key to any lock that you have. How do you do it? Note that you cannot send a key in an unlocked box, since it might be copied.Answer
- Mixing Tea and Coffee
- Start with a half cup of tea and a half cup of coffee. Take one tablespoon of the tea and mix it in with the coffee. Take one tablespoon of this mixture and mix it back in with the tea. Which of the two cups contains more of its original contents?Answer