The Seashell Press
Noggintwisters

Table of Contents

Sample Chapter

Interactive Puzzles
Three Pennies
Monty Hall Problem
The Brooklyn Bridge
Einstein's Neighborhood

Sample Chapter

World's Smartest Person

Imagine for the next few puzzles that you are The Smartest Person in the World, and have set up your little consulting practice in one of those old brick buildings overlooking the food stalls at Boston's Quincy Market. People call you day and night, and for a small fee you help them wiggle out of whatever mess they've gotten themselves into. It is the beginning of your day. No sooner do you pour your first cup of coffee than the phone starts ringing:


three lights

The first caller this morning is from Brunswick, Maine, where she has just inherited a nineteenth century lighthouse from her grandfather, an amateur scientist who blew himself to smithereens in a chemistry experiment at the age of 93. The caller says there are three switches near the front door marked simply "top floor lights", but which one goes to which light? There are eight flights of stairs up to the top, and she only wants to climb them once. How can she set the switches so when she does climb to the top floor she can tell immediately which switch goes to which light bulb?

hint
Obviously there are two states that can be set by the switches: on and off. But if you think about it, there is a third state you can create downstairs that can be detected up on the light platform.


arthurs socks

Arthur has 6 black socks and 6 brown socks mixed together in one drawer. But packing for a trip at dawn, he cannot tell them apart. How many socks must he take to make sure that when he crosses his legs in the next meeting, the others in the room will not burst out laughing.

hint
Two socks won't do it, since they could be of two different colors.


tomorrow

Two logic professors from a Kansas college call to say they have talked themselves into a terrible tangle.

"When the day after tomorrow is 'yesterday'," says the first one, who sounds a little confused, "then 'today' will be as far from Sunday as that day was which was 'today' when the day before yesterday was 'tomorrow'! So we need your help. What day is it today?"

hint
Sometimes the answer is easy but the question is hard.


measuring water

To make pancakes on his hiking trip, your brother-in-law says he needs exactly 4 ounces of water from a mountain stream. But he only has a 3-ounce cup and a 5-ounce cup. How does he measure the water?

hint
This is an old and well-loved puzzle from the nineteenth century, originally told about a farmer who travels through the neighborhood selling raw milk out of a pail. But the clever insight was always there: The trick is to see that the only way to measure 2 ounces or 4 ounces with a 3-ounce cup and a 5-ounce is to subtract one from the other.


busy boy

Fiorello (“The Pro") Provolone is pleading with the principal that he only has time for school one day a week. He pushes his calculations across the desk, and the flustered principal reads them to you over the phone:

Current commitments:
Eat (3 hours/day) 45 days
Sleep (8 hours/day) 122 days
Outdoor exercise (2 hours/day) 30 days
Saturdays and Sundays 104 days
Major holidays 7 days
Summer church camp 30 days
  338 days

Fiorello is a known troublemaker, and in his heart the principal hopes the calculations are correct. But are they?

Photo: Actor Matthew Broderick from the movie, "Ferris Bueller's Day Off", 1986.


two barbers

It is 10 o'clock in the morning in Indiana, and a location scout for a revival of the Twilight Zone television series needs a haircut before meeting the mayor. But it is a small town with only two barbers. One is an older man with a shabby haircut, outdated chairs and just the bare necessities. The other barber has a nice haircut, new razors and a lot of nice chairs. Which one should he go to?

hint
If the answer was the obvious one, this wouldn't be a puzzle. So the question really is, what reason do you give your client for going to the shabby guy?


vanishing dollar

It's lunchtime and you get a call from a college kid in Chicago. He and two friends have chipped in to buy a $15 pitcher of beer at a roadhouse they go to all the time. The owner, seeing his good customers again, decides to send the waiter back with $5. But your client says the waiter only returned $1 to each of them and admits pocketing $2. "I can't figure it out. If each of us ended up putting in $4, and the waiter stole $2, where did the other $1 go?"

hint
Your client has been drinking more than his share. There is nothing wrong with the money; the problem is all in how he is doing his math.


m ixed socks

In putting three sock boxes on the storeroom shelf, someone has accidentally switched the labels ("Red Socks", "Green Socks", and "Rd and Grn Socks") so that each label is now incorrect. How can you put the labels back on the right boxes by taking only one sock out of one box?

hint
This puzzle, like many of the clever puzzles we find, depends for its solution on a negative deduction.


pricing fruit

The next call comes in from a young man who his helping out his girlfriend's father in his vegetable stand in New York's Little Italy. He is supposed to price the fruit but he doesn't understand the rule her father is following. "And I can't ask him. He already thinks I am a doofus." An orange is priced at 18 cents, a pineapple costs 27 cents and a grape costs 15 cents. So what should be the price for a mango?

hint
Look carefully at the two pieces of information you have about each fruit: the name and the price.


shaking hands

Frantic call from Senator Fogbottom's body man. The Senator is going into a political fundraiser where he will have to shake hands with each of the 49 guests, and each of them must shake hands at least once with every other guest. These days politicians and contributors all use hand sanitizer—any serious player would—and they want the Senator's staff to make it available. How many handshakes will the 50 people do?

hint
It's not complicated. Each person has to shake hands with each of the other 49 persons.


desk calendar

The caller was whispering: "I am being interviewed for a top job at a high tech company in Seattle. It's going pretty well, but the boss has given me one last problem. On her desk are two six-sided cubes and every day she arranges them so that the front faces show the current day of the month, 01 through 31. Without touching the cubes, what numbers are on each of the cubes? She has left the office for a minute, but she is coming right back. What do I say?"

hint
On the sides you can see, the first cube has 0, 1 and 2. The second cube has 2, 7 and 8. What numbers are on the hidden sides?


weighing gold

“Ciao, Baby! What time is it there? Yeah, well we're dancing down the Via Condotti. Monfortino all around, Baby!" The head of detectives from the Rome Police, a frequent caller, has recovered the gold from the great Italian bullion heist of 1996. But there is evidence that one of nine ingots has been shaved and is lighter than the others. All he has is a simple balance scale taken from a drug bust and only a few minutes to figure out which ingot it is. What is the fastest way to find the light brick?

hint
Remember there are three stacks, one on each end of the balance, and one on the table.


copper wire

A salvage worker in San Diego calls from an abandoned freighter where two valuable copper cables, a foot apart, hang down 30 feet from the ceiling of an empty cargo hold. One cable is black, the other red. With only a pair of cable cutters, how can he recover the most cable?

hint
He figures he can climb up the black cable and cut the red one near the ceiling, but how much of the black cable can he get without falling too far to the floor below?


give me a sign

An old client and his friends, hiking through the ancient countryside of Dorset in Southwest England, have knocked over a four-way signpost, and now they don't know how to orient it again. You remember an old story about Napoleon in a similar fix. He was in the midst of battle and his troops were massed at a critical intersection in an unfamiliar area. No one could tell which way was Le Havre, Metz, Waterloo or Paris. Then Napoleon rode up, looked around, and set the post correctly in the ground. How did he know the right direction?

hint
Napoleon never forgot where came from.


utilities

A contractor in Florida has laid out the grid for his new development, but now is stumped. He has to run water, gas and electricity from the end of the street to each of the first three houses, without any pipe or line crossing any other pipe or line.

hint
Known in graph theory as the "utilities problem", this puzzle has been around for at least a hundred years and there is no known solution without a trick.


finding north

The next caller is at a crossroads in the wheat fields of the Midwest on a cloudy afternoon, and he is lost. He has a map, but the horizon is all amber waves of grain and the roads all look alike. With only his father's pocket watch, how can he tell which one will take him north?

The painting is "Gray and Gold", by John Rogers Cox, Cleveland Museum

hint
The sun rises in the east and sets in the west, but that changes with the latitudes and time of day. Moss usually grows on the north side of trees, moist, shady and least likely to feel the sun, but there are no trees around.


light room

"Help. I am in a dark room with a candle, a wood stove and a gas lamp. I only have one match, so what do I light first?"

hint
Honestly, you wonder how otherwise intelligent people wander into such difficulties. But you bite your tongue and give the answer.


3d pool

Your young client in Chicago has moved with his friends to the local pool hall, and, with more joy than wisdom, he calls you again. "Hey, if I arrange 10 billiard balls in a traditional triangular rack, guess how many more balls I can add to the stack to form a pyramid?"

hint
Count the spaces in between.


chinese checker

Three math majors at Vassar College call to get help settling the following bet: When the Chinese government decided it wanted more men and fewer women in the population, one proposal was to declare that any family that gave birth to a girl would be forbidden to have any more children. Thus families might have several boys, but no family would have more than one girl. Soon the men would outnumber the women. Would that work?

hint
This puzzle was developed by George Gamow and Marvin Stern, and was originally presented as a Sultan who wanted to increase the ratio of women to men so men could have more wives. Interesting idea, but the question remains.


seating suzie

Suzie, a lively and attractive girl, invites three boyfriends to the ball game. But the boys are jealous of each other. Biff will sit next to Suzie, but not next to Buck, and Buck will not sit next to Bob. Now she calls you in a panic. Who should sit where?

Photo: The gold seat above marks where Kirby Puckett's famous game-winning home run landed during the 1991 World Series in the Minneapolis Metrodome.

hint
First sit Biff next to Suzie.


norway weather

Last call of the day: “It's midnight over here in Norway, and it’s raining. Am I going to have sunny weather for spear fishing in 72 hours?"

hint
You have access to all the forecasts, but in this case the answer is easy.

Another day, another dollar. The thing about consulting is that the problems people bring you are often simple, but the answer is not obvious until the question is asked aloud. Take the rest of the day off and go across the street for dinner at Durgin Park.