The Monty Hall Problem

Suppose you’re a contestant on Let’s Make a Deal. Monty Hall shows you three doors. One hides a sports car; the other two hide goats. You choose Door #1.

Before opening Door #1, though, Monty opens Door #3, revealing a goat. Now you can stick with Door #1 or switch to Door #2. Which should you do?

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You should switch to Door #2. At the start, each door had a one-third chance of hiding the car. You chose Door #1, accepting a two-thirds chance that the car was really behind Door #2 or Door #3. In revealing the goat behind Door #3, Monty has helped you by removing that door from contention. Therefore the two-thirds chance now rests entirely with Door #2. This is counterintuitive, but it’s true. If you picture the universe of possibilities, you’ll see that in two-thirds of the cases you initially pick a goat, and Monty shows you where the car is by revealing the other goat. Only in one-third of the cases will you pick the car correctly on the first move, when switching is a bad idea.

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May 3, 2006May 23, 2013 | Puzzles

Hotel Puzzle

Three men stop at a hotel and agree to share a room for $30. Each gives the desk clerk $10.

Later, the clerk realizes he’s overcharged them for the room by $5. He gives the bellboy five $1 bills and tells him to return the money to the three men. The unscrupulous bellboy keeps $2 for himself and gives $1 to each of the three men.

So the men paid $9 each for the room, for a total of $27. The bellboy has $2. What happened to the other dollar?

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There’s actually no difficulty here. The desk clerk has $25, the guests have $3, and the bellboy has $2. The “trouble” arises only because we’re trying to add the bellboy’s $2 to the guests’ $27. Instead we should subtract it, giving $25 for the clerk, which is correct. In effect, the men paid $27 for a $25 room, and the clerk gave the change to the bellboy.

April 27, 2006January 14, 2013 | Puzzles

No Tips Either Way

Okay, you’re a chef. Which of these trays was requested for a singer’s dressing room, and which is the last meal of a Texas death-row inmate?

A. Neil Diamond (“Love on the Rocks”)
B. Nelly (“Hot in Herre”)
C. Smokey Robinson (“Tears of a Clown”)
D. B.B. King (“The Thrill Is Gone”)
E. Cornelius Goss (beat a Dallas homeowner to death with a board)
F. Gerald Mitchell (shotgunned two customers during a Houston drug deal)
G. James Collier (shot two Wichita Falls residents while stalking his daughter)
H. James Powell (raped and murdered a 10-year-old in Beaumont)
I. Paul Nuncio (strangled a 61-year-old in Plainview)

1. BBQ chicken wings, chips, fruit, ginger ale
2. 1 apple, 1 orange, 1 banana, coconut, peaches
3. One pot of coffee
4. Enchiladas, burritos, chocolate ice cream, cantaloupe (whole, split in half)
5. Chinese takeout, coffee
6. 1 bag of assorted Jolly Ranchers
7. Baked salmon, french fries, fruit platter, salad, soda
8. Nothing
9. Thirty jumbo shrimp, cocktail sauce, baked potato, French fries, ketchup, butter, one T-bone steak, one chocolate malt, one gallon of vanilla ice cream, and three cans of Big Red

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A. Neil Diamond (“Love on the Rocks”) 5. Chinese takeout, coffee B. Nelly (“Hot in Herre”) 7. Baked salmon, french fries, fruit platter, salad, soda C. Smokey Robinson (“Tears of a Clown”): 1. BBQ chicken wings, chips, fruit, ginger ale D. B.B. King (“The Thrill Is Gone”) 8. Nothing E. Cornelius Goss (beat a Dallas homeowner to death with a board): 2. 1 apple, 1 orange, 1 banana, coconut, peaches F. Gerald Mitchell (shotgunned two customers during a Houston drug deal) 6. 1 bag of assorted Jolly Ranchers G. James Collier (shot two Wichita Falls residents while stalking his daughter) 9. Thirty jumbo shrimp, cocktail sauce, baked potato, French fries, ketchup, butter, one T-bone steak, one chocolate malt, one gallon of vanilla ice cream, and three cans of Big Red H. James Powell (raped and murdered a 10-year-old in Beaumont) 3. One pot of coffee I. Paul Nuncio (strangled a 61-year-old in Plainview) 4. Enchiladas, burritos, chocolate ice cream, cantaloupe (whole, split in half)

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What’s Odd?

How quickly can you find out what is unusual about this paragraph? It looks so ordinary that you would think that nothing was wrong with it at all and, in fact, nothing is. But it is unusual. Why? If you study it and think about it you may find out, but I am not going to assist you in any way. You must do it without coaching. No doubt, if you work at it for long, it will dawn on you. Who knows? Go to work and try your skill. Par is about half an hour.

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The paragraph does not contain the letter e. I’m going to have to start finding some harder puzzles!

April 8, 2006January 14, 2013 | Puzzles

Trick Mules Puzzle

Sam Loyd was only 17 when his “Trick Mules Puzzle” swept the country in 1858. He finally sold it to P.T. Barnum for $10,000.

Print this page and cut out the three pieces along the dashed lines. Now arrange them so that it looks like each jockey is riding a mule. You may overlap the pieces, but you mustn’t fold them.

It’s harder than it looks.

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April 4, 2006January 14, 2013 | Puzzles

Puzzling Brothers

Tom and Dick were born on the same day of the same year to same mother and father. They look almost exactly alike, yet they are not twins. How can this be?

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They’re two members of a set of triplets.

March 14, 2006January 14, 2013 | Puzzles

Okay

Can you name a common English word, besides sugar, in which the initial s is pronounced sh?

February 25, 2006October 5, 2006 | Puzzles

The Underpass

A large truck had become wedged under an underpass. The driver couldn’t move it backward or forward, and traffic was beginning to back up behind it.

He was on the point of desperation when a little boy approached him and offered a suggestion. A few minutes later the truck was on its way. What did the boy tell the driver?

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Let some air out of the tires.

February 20, 2006January 14, 2013 | Puzzles

Rig Latin

In the dusty street of an Old West mining town, a classics professor was stunned to find a post bearing this inscription:

TOTI
EHORS
ESTO

What was the post for?

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“TO TIE HORSES TO.”

February 10, 2006January 14, 2013 | Puzzles

Down, Over, Up

If you start at the North Pole and walk one mile south, one mile east, and one mile north, you’ll find yourself back at your starting point.

The North Pole is not the only point with this property on Earth’s surface. In fact, there are any number of such points. Where are they?

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There’s a ring of such points around the South Pole — from any one of them you’d walk south, march in a circle around the pole, and return north to your starting point. (Further solutions involve circling the pole multiple times.)

February 6, 2006January 14, 2013 | Puzzles