Six friends were on a large sail boat far out to sea. They had the usual safety gear on board, including an inflatable life raft and personal flotation vests (life jackets). They decided to go for a swim in the calm waters, and one by one jumped over the edge. One had a plastic float toy, another a diving mask, and only one was wearing a life jacket. One man was wearing denim shorts with a knife on the belt, and the rest simply had on their swim suits. You may recognize this as a movie which was supposedly based on a true story.
They realized too late that nobody had put the ladder down. The sides of the boat were smooth polished fiberglass and sloped out over their heads. It was at least six feet up to the railing. They tried jumping high enough, but soon they were tired and cold. A breeze blew a jacket to the edge above, and a sleeve hung low enough that one of the men was able to grab it and pull the nylon jacket into the water with them. There was no land in sight. What could they do to save themselves?

The More Obvious Solutions

As mentioned, they tried jumping out of the water to reach the railing. As I recall, a couple of them even tried lifting another up, but they sunk into the water as they lifted her. Those, and swimming around the boat to see if there was anything hanging down to climb up on, were what I would consider the expected responses.
A bit more creative, although still a fairly "linear" solution, was to use their swim suits, and the jacket tie to create a "rope" that could be thrown up to the railing. Once tangled or caught on the railing, it could then be climbed. In the movie, it took them hours to think of this, and after one attempt during which the clothing broke halfway through the climb, they gave up, as people strangely do in movies.

The More "Lateral Thinking" Examples

Lateral thinking, remember, is moving away from the usual logic and linear line of reasoning. For example, it is logical to think about jumping up to reach the railing, and to help a person do that. A more creative or lateral approach would be to question the logic of using people as "muscle" for this attempt. What else could they be? Flotation.
One man could have leaned over and held his hands on his knees to provide a platform (his back) for another to climb on. Meanwhile, the others could each take a deep breath and swum down under the first to provide more flotation. They could have held the inflatable toy and life jacket under there as well. This might have kept the "platform" man floating high enough for the climber to stand on and reach the railing.
Lateral thinking, then, is sometimes about using what you have in unexpected ways. The knife, for example, might be used more conventionally to cut strips from the clothing and webbing from the life jacket to make a rope - not a bad idea either. But a more "lateral" though is for a man to pound it into the hull of the boat and use it to hang from while the lightest woman climbs over him to the railing.
But to think in lateral or non-linear ways also means to challenge the whole line of thought that the pursuit of a solution is based on. In this case, that line of thought is that they had to get back on the boat. Of course it is natural to think that is the only way to survive, but what if it wasn't? What if they don't actually need the boat?
Those kind of questions can sometimes lead to the most creative solutions. In this case, for example, had they challenged their assumption that the boat was so important, this lateral thinking may have lead to a very creative solution: Use the knife to cut a hole in the hull and sink the boat. As the boat got lower, they could have scrambled aboard and retrieved the life raft and supplies before it sank completely.
In the movie the knife is lost, and eventually four of the six died. The remaining two are saved using a broken piece of the face of the diving mask. This is jammed into a crack where the mechanical ladder normally opens, and the man hangs on it while the woman climbs over him and reaches the railing. Of course, since I did not mention the crack, this wouldn't be one of your solutions. But it is one of the better lateral thinking examples in this realistic scenario.

You are probably most familiar with lateral thinking problems which are puzzles or riddles. They lead you to make certain assumptions, and to solve them you have to look at those assumptions you're making and try to get beyond them. Here is a short example of this type:
The book store owner used one book to destroy thousands of others - all in one day. How did he do this? A lateral thinking puzzle like this relies on setting your thoughts in a certain direction. In this case, the idea of a "book store owner" encourages you assume that a book one reads was used to destroy the others. Drop that assumption and you might find the solution - the man used a book of matches to burn all the other books.
Puzzles of this type are good mental exercise, and fun, but fortunately not all lateral thinking problems are word play or simple riddles. In fact, many are designed to require or encourage creative thinking in ways more applicable to actual situations. This type often has many solutions which are valid.
Some may not like the inconclusive nature of this kind of puzzle or problem. They want one definitive solution, so they know they're "right" once they have an answer. However, these more open-ended lateral thinking problems are just as good for exercising one's creativity, and the thinking skills developed from working on them may be more applicable to everyday life, where there is rarely one definitive solution to a problem.

Situational Thinking Problems

This type usually involves a scenario or situation which is explained, along with a goal. Suppose, for example, you need to get a basketball out of a 12-foot deep pit. That's the goal. The situation? The pit has smooth cement for the floor and walls, and it is square, about four feet per side. You're alone and have only what you are wearing, including whatever is in your pockets at the moment. How can you get the basketball out using only what has been described?
Like any good lateral thinking problem this requires you to think "laterally," which means coming at the problem from other angles, as opposed to the more traditional linear or logical way. You have to use what you have, but in ways that these things are not normally used.
You might, for example, make a "basket" out of your t-shirt, tying your shoelaces to it around the edges. Unravel the threads from your socks and you can make a string to lower the "basket." Then move the basketball onto it and then pull it up to you. A shoe hung on the end of a string made of strips of clothing might work to "kick" the ball into place, rolling it onto your shirt.
You might also use a piece of paper from your pocket. Chew it up, drop it onto the ball using shoe laces or clothing, and when it dries it would perhaps "glue" the line to the ball, allowing it to be lifted. You might "chimney" your body up and down the pit to get the ball (if you are tall enough), as climbers do between rock walls. Certainly there are other possibilities too.
Of course, life itself presents us with many lateral thinking problems, if we approach situations creatively. A judge in a Michigan child custody case could have followed the traditional thinking about how much time the children would spend at each parent's place, but he ruled that the children would stay right where they were in the home they knew. The parents would each get their own place and move in with the kids on alternating weeks. Now that's a good example of applying lateral thinking to real life problems.

lateral thinking

A Collection of Quant Riddles With (some) Answers

The quant riddles or logic or lateral puzzles below have been accumulated from the internet and emails that I receive. They are designed to help training for job or university interviews or just training your brain. The internet is littered with this kind of thing but the answers can be a little harder to find so I've thought about all of them and the ones that I know the answer to can be clicked on and have little at the end. Questions 3 & 5 are probably the easiest and a good place to start. I've coloured them Red, Amber and Green to indicate Very Hard, Quite Hard and Not so Hard. So that's it good luck....

This problem is actually damn hard, I don't know why I put it first. You are given a set of scales and 12 marbles. The scales are of the old balance variety. That is, a small dish hangs from each end of a rod that is balanced in the middle. The device enables you to conclude either that the contents of the dishes weigh the same or that the dish that falls lower has heavier contents than the other. The 12 marbles appear to be identical. In fact, 11 of them are identical, and one is of a different weight. Your task is to identify the unusual marble and discard it. You are allowed to use the scales three times if you wish, but no more.  Note that the unusual marble may be heavier or lighter than the others. You are asked to both identify it and determine whether it is heavy or light.

You are given a set of scales and 90 coins. The scales are of the same type as above. You must pay $100 every time you use the scales. The 90 coins appear to be identical. In fact, 89 of them are identical, and one is of a different weight. Your task is to identify the unusual coin and to discard it while minimizing the maximum possible cost of weighing (another task might be to minimizing the expected cost of weighing). What is your algorithm to complete this task? What is the most it can cost to identify the unusual coin?

You are a bug sitting in one corner of a cubic room. You wish to walk (no flying) to the extreme opposite corner (the one farthest from you). Describe the shortest path that you can walk.

A mythical city contains 100,000 married couples but no children. Each family wishes to “continue the male line”, but they do not wish to over-populate. So, each family has one baby per annum until the arrival of the first boy. For example, if (at some future date) a family has five children, then it must be either that they are all girls, and another child is planned, or that there are four girls and one boy, and no more children are planned. Assume that children are equally likely to be born male or female. Let p(t) be the percentage of children that are male at the end of year t. How is this percentage expected to evolve through time?

How many degrees (if any) are there in the angle between the hour and minute hands of a clock when the time is a quarter past three?

There are 100 light bulbs lined up in a row in a long room. Each bulb has its own switch and is currently switched off. The room has an entry door and an exit door. There are 100 people lined up outside the entry door. Each bulb is numbered consecutively from 1 to 100. So is each person. Person No. 1 enters the room, switches on every bulb, and exits. Person No. 2 enters and flips the switch on every second bulb (turning off bulbs 2, 4, 6, …). Person No. 3 enters and flips the switch on every third bulb (changing the state on bulbs 3, 6, 9, …). This continues until all 100 people have passed through the room. What is the final state of bulb No. 64? And how many of the light bulbs are illuminated after the 100th person has passed through the room?

A windowless room contains three identical light fixtures, each containing an identical light bulb. Each light is connected to one of three switches outside of the room. Each bulb is switched off at present. You are outside the room, and the door is closed. You have one , and only one, opportunity to flip any of the external switches. After this, you can go into the room and look at the lights, but you may not touch the switches again. How can you tell which switch goes to which light?

What is the smallest positive integer that leaves a remainder of 1 when divided by 2, remainder of 2 when divided by 3, a remainder of 3 when divided by 4, … and a remainder of 9 when divided by 10?

In a certain matriarchal town, the women all believe in an old prophecy that says there will come a time when a stranger will visit the town and announce whether any of the men folks are cheating on their wives. The stranger will simply say “yes” or “no”, without announcing the number of men implicated or their identities. If the stranger arrives and makes his announcement, the women know that they must follow a particular rule: If on any day following the stranger’s announcement a woman deduces that her husband is not faithful to her, she must kick him out into the street at 10 A.M. the next day. This action is immediately observable by every resident in the town. It is well known that each wife is already observant enough to know whether any man (except her own husband) is cheating on his wife. However, no woman can reveal that information to any other. A cheating husband is also assumed to remain silent about his infidelity. The time comes, and a stranger arrives. He announces that there are cheating men in the town. On the morning of the 10th day following the stranger’s arrival, some unfaithful men are kicked out into the street for the first time. How many of them are there?

You and I are to play a competitive game. We shall take it in turns to call out integers. The first person to call out “50” wins. The rules are as follows: The player who starts must call out an integer between 1 and 10, inclusive; A new number called out must exceed the most recent number called by at least one and by no more than 10. Do you want to go first, and if so, what is your strategy?

You are to open a safe without knowing the combination. Beginning with the dial set at zero, the dial must be turned counter-clockwise to the first combination number, (then clockwise back to zero), and clockwise to the second combination number, (then counter-clockwise back to zero), and counter-clockwise again to the third and final number, where upon the door shall immediately spring open. There are 40 numbers on the dial, including the zero. Without knowing the combination numbers, what is the maximum number of trials required to open the safe (one trial equals one attempt to dial a full three-number combination)?

Inside of a dark closet are five hats: three blue and two red. Knowing this, three smart men go into the closet, and each selects a hat in the dark and places it unseen upon his head. Once outside the closet, no man can see his own hat. The first man looks at the other two, thinks, and says, “I cannot tell what colour my hat is.” The second man hears this, looks at the other two, and says, “I cannot tell what colour my hat is either.” The third man is blind. The blind man says, “Well, I know what colour my hat is.” What colour is his hat?

You are standing at the centre of a circular field of radius R. The field has a low wire fence around it. Attached to the wire fence (and restricted to running around the perimeter) is a large, sharp-fanged, hungry dog. You can run at speed v, while the dog can run four times as fast. What is your running strategy to escape the field?

You have 52 playing cards (26 red, 26 black). You draw cards one by one. A red card pays you a dollar. A black one fines you a dollar. You can stop any time you want. Cards are not returned to the deck after being drawn. What is the optimal stopping rule in terms of maximizing expected payoff? Also, what is the expected payoff following this optimal rule?

Why is that if p is a prime number bigger than 3, then p2-1 is always divisible by 24 with no remainder?

You have a chessboard (8×8) plus a big box of dominoes (each 2×1). I use a marker pen to put an “X” in the squares at coordinates (1, 1) and (8, 8) - a pair of diagonally opposing corners. Is it possible to cover the remaining 62 squares using the dominoes without any of them sticking out over the edge of the board and without any of them overlapping? You cannot let the dominoes stand on their ends.

You have a string-like fuse that burns in exactly one minute. The fuse is inhomogeneous, and it may burn slowly at first, then quickly, then slowly, and so on. You have a match, and no watch. How do you measure exactly 30 seconds?

Can the mean of any two consecutive prime numbers ever be prime?

How many consecutive zeros are there at the end of 100! (100 factorial). How would your solution change if there problem were in base 5? How about in Binary???

How can this be true???? Have a look at the picture (click to enlarge.) All the lines are straight, the shapes that make up the top picture are the same as the ones in the bottom picture so where does the gap come from????

A man is in a rowing boat floating on a lake, in the boat he has a brick. He throws the brick over the side of the boat so as it lands in the water. The brick sinks quickly. The question is, as a result of this does the water level in the lake go up or down?

You have a 3 and a 5 litre water container, each container has no markings except for that which gives you it's total volume. You also have a running tap. You must use the containers and the tap in such away as to exactly measure out 4 litres of water. How is this done?

I have three envelopes, into one of them I put a £20 note. I lay the envelopes out on a table in front of me and allow you to pick one envelope. You hold but do not open this envelope. I then take one of the envelopes from the table, demonstrate to you that it was empty, screw it up and throw it away. The question is would you rather stick with the envelope you have selected or exchange it for the one on the table. Why? What would be the expected value to you of the exchange?

You're a farmer. You're going to a market to buy some animals. On the market there are 3 types of animals for sale. You can buy: Horses for £10 each, goats for £1 each and ducks, you get 8 of these per bunch and each bunch costs £1. The aim is to acquire 100 animals at the cost of £100, what is the combination of horses, goats and duck that allows you to do this? (You must buy at least one of each.)

Adam, Bob, Clair and Dave are out walking: They come to rickety old wooden bridge. The bridge is weak and only able to carry the weight of two of them at a time. Because they are in a rush and the light is fading they must cross in the minimum time possible and must carry a torch (flashlight,) on each crossing. They only have one torch and it can't be thrown. Because of their different fitness levels and some minor injuries they can all cross at different speeds. Adam can cross in 1 minute, Bob in 2 minutes, Clair in 5 minutes and Dave in 10 minutes. Adam, the brains of the group thinks for a moment and declares that the crossing can be completed in 17 minutes. There is no trick. How is this done????

A man has built three houses. Nearby there are gas water and electric plants. The man wishes to connect all three houses to each of the gas, water and electricity supplies. Unfortunately the pipes and cables must not cross each other. How would you connect connect each of the 3 houses to each of the gas, water and electricityic supplies???

How many squares are there on a chessboard?? (the answer is not 64) Can you extend your technique to calculate the number of rectangles on a chessboard.

3 men go into a hotel. The man behind the desk said the room is $30 so each man paid $10 and went to the room. A while later the man behind the desk realized the room was only $25 so he sent the bellboy to the 3 guys' room with $5. On the way the bellboy couldn't figure out how to split $5 evenly between 3 men, so he gave each man a $1 and kept the other $2 for himself. This meant that the 3 men each paid $9 for the room, which is a total of $27 add the $2 that the bellboy kept = $29. Where is the other dollar?

There were two men having a meal. The first man brought 5 loaves of bread, and the second brought 3. A third man, Ali, came and joined them. They together ate the whole 8 loaves. As he left Ali gave the men 8 coins as a thank you. The first man said that he would take 5 of the coins and give his partner 3, but the second man refused and asked for the half of the sum (i.e. 4 coins) as an equal division. The first one refused. They went to Ali and asked for the fair solution. Ali told the second man, "I think it is better for you to accept your partner's offer." But the man refused and asked for justice. So Ali said, "then I say that who offered 5 loaves takes 7 coins, and who offered 3 loaves takes 1 coin." Can you explain why this was actually fair???

A drinks machine offers three selections - Tea, Coffee or Random but the machine has been wired up wrongly so that each button does not give what it claims. If each drink costs 50p, how much minimum money do you have to put into the machine to work out which button gives which selection ? .

Dr. Kiran Mazumdar‐Shaw
Entrepreneur Dr. Kiran Mazumdar‐
Shaw, Chairman & Managing Director of
Bioon Ltd. She was educated at the Bishop
Cotton Girls School and Mount Carmel
College in Bangalore.
She founded Biocon India with a
capital of Rs.10,000 in her garage in 1978 ‐
the initial operation was to extract an
enzyme from papaya. Her application for
loans were turned down by banks then ‐
on three counts ‐ biotechnology was then a
new word, thecompany lacked assets, and
(most importantly) women entrepreneurs
were still a rarity. Today, her company is
the biggest biopharmaceutical firm in the
country.
In 2004, Biocon went for an IPO and the issue was over‐subscribed by over
30 times. Post‐IPO, Shaw held close to 40% of the stock of the company and was
regarded as India’s richest woman with an estimated worth of Rs. 2,100 crore (~U.S.
$ 480 million).
􀂾 Anu Aga
This woman became the Chairperson of
Thermax Engineering after the death of
her husband Rohinton Aga. The
company’s condition was critical at that
time. Its share price dipped to Rs. 36 from
Rs. 400. Anu Aga, the then Director of
Human Resource, Thermax, was
compelled to take charge of the company.
In order to make the company profitable, she brought a consultant from
abroad and restructured the company. The strategy worked and the company saw
profit again. She stepped down from the post of chairperson in 2004. Now, she
spends most of her time in social activities. Bombay Management Association
awarded her Management Woman Achiever of the Year Award 2002‐2003.
After retiring from Thermax, she took to social work, and 2010 was
awarded the Padma Shri (Social Work) by Govt. of India.

Dr. Kiran Mazumdar‐Shaw
Entrepreneur Dr. Kiran Mazumdar‐
Shaw, Chairman & Managing Director of
Bioon Ltd. She was educated at the Bishop
Cotton Girls School and Mount Carmel
College in Bangalore.
She founded Biocon India with a
capital of Rs.10,000 in her garage in 1978 ‐
the initial operation was to extract an
enzyme from papaya. Her application for
loans were turned down by banks then ‐
on three counts ‐ biotechnology was then a
new word, thecompany lacked assets, and
(most importantly) women entrepreneurs
were still a rarity. Today, her company is
the biggest biopharmaceutical firm in the
country.
In 2004, Biocon went for an IPO and the issue was over‐subscribed by over
30 times. Post‐IPO, Shaw held close to 40% of the stock of the company and was
regarded as India’s richest woman with an estimated worth of Rs. 2,100 crore (~U.S.
$ 480 million).
􀂾 Anu Aga
This woman became the Chairperson of
Thermax Engineering after the death of
her husband Rohinton Aga. The
company’s condition was critical at that
time. Its share price dipped to Rs. 36 from
Rs. 400. Anu Aga, the then Director of
Human Resource, Thermax, was
compelled to take charge of the company.
In order to make the company profitable, she brought a consultant from
abroad and restructured the company. The strategy worked and the company saw
profit again. She stepped down from the post of chairperson in 2004. Now, she
spends most of her time in social activities. Bombay Management Association
awarded her Management Woman Achiever of the Year Award 2002‐2003.
After retiring from Thermax, she took to social work, and 2010 was
awarded the Padma Shri (Social Work) by Govt. of India.

Indra Nooyi
Indian born American
businesswoman, Indra Krishnamurthy
Nooyi born October 28, 1955 is the
Chairperson and Chief Executive Officer
(CEO) of PepsiCo, one of the worldʹs
leading food and beverage companies.
On August 14, 2006, Nooyi was named
the successor to Steven Reinemund as
chief executive officer of the company
effective October 1, 2006. On February 5,
2007, she was named Chairperson,
effective May 2, 2007.
Nooyi joined PepsiCo in 1994 and was named president and CFO in 2001.
Nooyi has directed the companyʹs global strategy for more than decade and led
PepsiCoʹs restructuring, including the 1997 divestiture of its restaurants into
Tricon, now known as Yum! Brands. Nooyi also took the lead in the acquisition of
Tropicana in 1998, and merger with Quaker Oats Company, which also brought
Gatorade to PepsiCo. In 2007 she became the fifth CEO in PepsiCoʹs 44‐year
history.
Nooyiʹs key contributions include promoting and supporting socially
responsible business practices, including taking on one of the planetʹs most
pressing problems, climate change. Her commitment to global citizenship is
evidenced by her multi‐year growth strategy, ʺPerformance with Purposeʺ.
Nooyi was named on Wall Street Journalʹs list of 50 women to watch in 2007
and 2008, and was listed among Timeʹs 100 Most Influential People in The World
in 2007 and 2008. Nooyi has been named 2009 CEO of the Year by the Global
Supply Chain Leaders Group (GSCLG).