Number of words: 2,145

QUESTIONS

• How would you weigh a jet plane without using scales?

Elephant in boat strategy.

• Why are manhole covers round rather than square?

So that they can’t be pushed in accidentally

• Why do mirrors reverse right and left instead of up and down?

Because they are hung vertically

• Which way should the key turn in a car door to unlock it?

Clockwise – it’s easier for right handed people.

• Why is it that, when you turn on the hot water in a hotel, the hot water comes out instantly?

   Because there is a separate reverse hot water line from the heater to the farthest tap.

• How do they make M&Ms?

Replace it with Gems. Basically sprays and a kind of centrifuge grinding.

• If you are on a boat and toss a suitcase overboard, will the water level rise or fall?

Depends on the density of the suitcase. If it floats, the level remains the same. If it sinks, it will lower the water level slightly.

• How many piano tuners are there in the world?

Upper middle class houses * 0.1 / (50 * 20) = 5000

• How many gas stations are there in the United States?

     Number of vehicles / Number of vehicles serviced per pump per week

     Assuming that you go to a pump once a week.

• How much Mississippi River water flows past New Orleans each hour?

     Cross section Area * Velocity of water flow

• If you could remove any of the fifty U.S. states, which would it be?

Decide on criterion: Are we killing the people? Are we relocating them? Are we ceding them to another country?

• How many points are there on the globe where, by walking one mile south, one mile east, and one mile north, you reach the place where you started?

     Not just the North Pole, it can be a series of circles near the South Pole too. (With the first circle being 1 + 1(2*pi) miles from the south pole. Then you can also have another circle where you make two revolutions of the earth and return back to the same point ….etc )

• How many times a day do a clock’s hands overlap?

     23

• Mike and Todd have $21 between them. Mike has $20 more than Todd. How much does each have? You can’t use fractions in the answer.

     20.5 and 0.5 – the cents are not in fractions!

• How do you cut a rectangular cake into two equal pieces when someone has already removed a rectangular piece from it? The removed piece can be of any size or orientation. You are allowed just one straight cut.

Any cut as long as it is through the center of the removed rectangular piece. Alternatively, you could do a horizontal cut and slice it in two.

• Design a remote control for a Venetian blind.

     Two motions – rotate and lower. With associated sensors – to do these actions based on light conditions.

• Design a spice rack for a blind person.

     Braille lettering, auto dispensers.

• How would you test a saltshaker? [A toaster? A teakettle? An elevator?]

     From a consumer point of view, see what can go wrong. Dispensing, Filling, Identifying.

• How would you locate a specific book in a big library? There’s no cataloging system and no librarian to help you.

Develop a map. Through systematic sampling, locate a similar book – and concentrate your search in that area.

• Suppose you’re hired as an IRS agent. Your first job is to find out whether a nanny agency is cheating on its taxes. How would you do it?

Change it to chai tapri for Indian conditions. The idea is to check how much of milk is being used every day. Also number of customers visited in an hour etc.

• You have eight billiard balls. One of them is “defective,” meaning that it weighs more than the others. How do you tell, using a balance, which ball is defective in two weighings?

3 + 3. Then 1 + 1

• You have five jars of pills. All the pills in one jar only are “contaminated.” The only way to tell which pills are contaminated is by weight. A regular pill weighs 10 grams; a contaminated pill is 9 grams. You are given a scale and allowed to make just one measurement with it How do you tell which jar is contaminated?

5 pills from first jar, 4 pills from second jar…

• There are three ants at the three corners of a regular triangle. Each ant starts moving on a straight line toward another, randomly chosen corner. What is the probability that none of the ants collide?

     ¼

• There are four dogs, each at a corner of a large square. Each of the dogs begins chasing the dog clockwise from it. All of the dogs run at the same speed. All continuously adjust their direction so that they are always heading straight toward their clockwise neighbor. How long does it take for the dogs to catch each other? Where does this happen?

Spiral towards the center.

• A train leaves Los Angeles for New York at a constant speed of 15 miles an hour. At the same moment, a train leaves New York for Los Angeles on the same track. It travels at a constant 20 miles an hour. At still the same moment, a bird leaves the Los Angeles train station and flies toward New York, following the track, at a speed of 25 miles an hour. When it reaches the train from New York, it instantly reverses direction. It travels at the same speed until it reaches the train from Los Angeles, when it reverses again, and so forth. The bird flies back and forth between the two trains until the very moment they collide. How far will the bird have traveled?

= 25* Time taken for them to meet.

• You have 26 constants, labeled A through Z. Let A equal 1. The other constants have values equal to the letter’s position in the alphabet, raised to the power of the previous constant. That means that B (the second letter) = 2A = 21 = 2. C = 3B = 32 = 9, and so on. Find the exact numerical value for this expression:

(X-A) * (X-B) * (X-C) * … (X-Y)*(X-Z)

0

• Count in base negative 2.

There can’t be a negative base

• You have two jars and 100 marbles. Fifty of the marbles are red, and 50 are blue. One of the jars will be chosen at random; then 1 marble will be withdrawn from that jar at random. How do you maximize the chance that a red marble will be chosen? (You must place all 100 marbles in the jars.) What is the chance of selecting a red marble when using your scheme?

1 red marble in one jar. The rest all in the other jar. Chances are then ¾.

• You have a 3-quart bucket, a 5-quart bucket, and an infinite supply of water. How can you measure out exactly 4 quarts?

5 -3 gives you 2. Pour the two into the 3. Then fill in the 5 – and pour 1 into the 3, to leave 4 in the 5 quart bucket.

• One of your employees insists on being paid daily in gold. You have a gold bar whose value is that of seven days’ salary for this employee. The bar is already segmented into seven equal pieces. If you are allowed to make just two cuts in the bar, and must settle with the employee at the end of each day, how do you do it?

First cut – one piece wide, Second cut – Two pieces wide

• You have b boxes and n dollar bills. Seal the money in the boxes so that, without thereafter opening any box, you can give someone any requested whole amount of dollars, from 0 to n. What are the restrictions on b and n?

1, 3,7,15  …. 2^b-1.

• You have a bucket of jelly beans in three colors — red, green, and blue. With your eyes closed, you have to reach in the bucket and take out two jelly beans of the same color. How many jelly beans do you have to take to be certain of getting two the same color?

• You have three picnic baskets filled with fruit. One has apples, one has oranges, and the third has a mixture of apples and oranges. You cannot see the fruit inside the baskets. Each basket is clearly labeled. Each label is wrong. You are permitted to close your eyes and pick one fruit from one basket, then examine it. How can you determine.

Mixed basket.

• Every man in a village of fifty couples has been unfaithful to his wife. Every woman in the village instantly knows when a man other than her husband has philandered (you know how small towns are) but not when her own husband has (“always the last to know”). The village’s notolerance adultery statute requires that a woman who can prove her husband is unfaithful must kill him that very day. No woman would dream of disobeying this law. One day, the queen, who is known to be infallible, visits the village. She announces that at least one husband has been unfaithful. What happens?

The queen ups the number every day. No killings happen on the first 49 days, because that is information all the women folk had in any case. On day 50, all of them kill their husbands.

• An evil demon captures a large, unspecified number of dwarfs. At each dwarfs entry interview, the demon plants a red or green gem in the dwarf’s forehead. The demon informs the new recruit that he, the dwarf, has an unremovable red or green jewel in his forehead; that he, the demon, is not going to tell him which color, nor will anyone else (the dwarfs are strictly forbidden to speak); that one of the colors denotes sniveling company spies and the other color denotes those particularly luckless captives who are not even sniveling company spies; that the demon does not choose to tell him which color denotes which, nor will he tell him, ever. End of entry interview.

Every day the dwarfs line up in formation so that the demon can count them, just to make sure no one has escaped. One day the demon gets tired of the dwarfs and decides to get rid of them. He announces that he will set the dwarfs free, provided they all deduce the color of their gems. As a hint, he tells them that there is at least one dwarf with a red gem, and at least one with a green gem.

To earn their collective freedom, the dwarfs must signal wordlessly at the daily lineup. All of the dwarfs with red gems are to step one pace forward, while the dwarfs with green gems remain behind. If they are correct, then all the dwarfs are free to go back to their homes in the coal mines. If they are not correct, all the dwarfs will be slaughtered on the spot.

The dwarfs are free to take as long as they want to determine the colors of their gems. They are all perfectly logical, and all are dying to get back to their homes. What should they do?

The test spans across several days 1.

If on day 1, no one steps forward, it implies that there are more than 1 red gems.

If on day 2, no one steps forward, it implies that there are more than 2 red gems.

So on the nth day, when a red dwarf, who has seen n -1 other red dwarfs, all n will step forward.

• Four people must cross a rickety footbridge at night. Many planks are missing, and the bridge can hold only two people at a time (any more than two, and the bridge collapses). The travelers must use a flashlight to guide their steps; otherwise they’re sure to step through a missing space and fall to their death. There is only one flashlight. The four people each travel at different speeds. Adam can cross the bridge in one minute; Larry in two minutes; Edge takes five minutes; and the slowest person, Bono, needs ten minutes. The bridge is going to collapse in exactly seventeen minutes. How can all four people cross the bridge?

Trip 1: Adam and Larry cross over – 2 min

Trip 2: Adam crosses back – 1 min

Trip 3: Bono and Edge cross over – 10 min

Trip 4: Larry crosses back – 2 min

Trip 5: Adam and Larry cross over – 2 min

Excerpted from page numbers80-86 of ‘How Would You Move Mount Fuji?’ by William Poundstone.