Some of these are logic puzzles; others are more in the category of brain teasers or bad jokes. Enjoy!
1. An explorer is captured by a band of vicious (but very logical) natives.
Their chief tells him:
"You may make a single, declarative statement. If
you make any other kind of statement, you will be beheaded. If what you
say is true, you will be stabbed. If what you say is false, you will be
thrown off the cliff."
What did the explorer say that saved his life?
2. If 10 computer science students can eat 10 hamburgers in 10 minutes, how long will it take 20 CS students to eat 20 hamburgers?
3. The annual "We Love Math Jamboree" is known for its variety of activities, including a one-mile cross-campus footrace. Student A takes off like a shot, running the entire course. Student B, taking his time, ambles along at a leisurely stroll, stopping to chat with friends along the way. Yet Student B crosses the finish line first. How?
4. How many times can you subtract 2 from 24?
5. Three people are in a room. All are blindfolded. In the room there is a box containing 5 headbands, 3 of gold and 2 of silver. Each person, working blind, selects a headband and puts it on, so none knows what type of headband they (or the others) are wearing.
The first person removes the blindfold, looks around, says "I don't know what kind of headband I have on," and puts the blindfold back on.
The second person removes the blindfold, looks around, says "I don't know what kind of headband I have on," and puts the blindfold back on.
Without removing the blindfold, the third person says, "I know what kind of headband I have on."
What type of headband did the third person have on, and how did he know?
6. You are in a small town, and in desperate need of a haircut. The town has two barbers. You notice the quality of haircut that each barber personally has. One barber has a neat, professional-looking style. The other's hair looks like it was cut by a drunken sheep-shearer using garden clippers.
Which barber do you select, and why?
7. Three businessmen (Abner, Bill, and Charlie) meet every day for lunch.
If Abner orders a martini, so does Bill.
Either Bill or Charlie always order a martini, but
never both at the same lunch.
Either Abner or Charlie, or both, always order a
martini.
If Charlie orders a martini, so does Abner.
From the above, conclude who among them will order a martini on any given day.
8. A set of chess pieces consists of 16 white pieces and 16 black pieces. Suppose we take all 32 pieces, throw them into a box, and shake them up. We now pull pieces out of the box two at a time. If both pieces are white, we put them into a white pile. If both pieces are black, we place them into a black pile. If the two pieces are of different colors, we discard them. We continue until all 32 pieces have been removed from the box.
Find the probability that the white pile and black pile will contain an equal number of pieces.
9. [Gardner] A farmer has 20 cows, 40 pigs, and 60 horses. How many horses does he have if you call the cows horses?
10. There are three light switches in the basement of a house, which
control three lights located on the second floor. You do not know which
switch controls which light. Obviously, you can throw a switch, then go
upstairs and check the lights to see which light that switch controls;
then go back downstairs, throw another switch, etc. There is an easier
way, though. Give an algorithm by which you can go to the basement once,
go upstairs to inspect the lights once, and determine which switch
controls which light, for all three switches.