Collection of Quant
Riddles With (some)
quant riddles or logic or lateral puzzles 1-19 appear in the book
'Heard on The Street: Quantitative Questions from Wall Street Job
Interviews' by Timothy Falcon Crack PhD available on his
website the rest 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 them all and answered all but one. I've added a 'Helpful Hint' button to each question. I've tried to keep the clues appropriate to the difficulty of the question but don't feel you have to read the whole thing, they add ideas incrementally. Questions 3 & 5 are probably the easiest and a good place
start. I've coloured them Red, Amber and Green
to indicate Very
Hard, Quite Hard
and Not so Hard together with the indicator on the right. The difficulty is very subjective, it's only a guide, but they all offer something in teaching you the ideas and tricks used to solve them.
So that's it good luck....
problem is actually damn hard, I don't know why I put it first.
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.
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.
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
- You are
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.
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
- 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
flips the switch on every second bulb (turning off
bulbs 2, 4,
6, …). Person No. 3 enters and flips the switch on every
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 so on up to a remainder of 9
- 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
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
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
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
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
- 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
hat is either.” The third man is blind. The blind man says,
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
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???
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?
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
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
- 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:
£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
- 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
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
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
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 =
is the other dollar?
There were two men having a
meal. The first man brought 5 loaves of bread, and the second brought
third man, Ali, came and joined them. They together ate the whole 8
he left Ali gave the men 8 coins as a thank you. The first man said
would take 5 of the coins and give his partner 3, but the second man
and asked for the half of the sum (i.e. 4 coins) as an equal division.
first one refused.
They went to Ali and asked
for the fair solution. Ali told the second man, "I think it is better
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
and who offered 3 loaves takes 1 coin."
you explain why this was
- 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?
- Consider a standard chess board. What is the diameter of the largest circle that can be drawn on the board whilst only drawing on the black squares. Hint: This problem is theoretical, so a line passing from one black square directly into it's diagonal neighbour through the intersecting corners is considered to have stayed within the black squares, the lines are infinitely thin.
- Two creepers, one jasmin and other rose, are both climbing up and round a cylindrical tree trunk. jasmine twists clockwise and rose anticlockwise, both start at the same point on the ground. before they reach the first branch of the tree the jasmine had made 5 complete twists and the rose 3 twists. not counting the bottom and the top, how many times do they cross?
- Assuming i wish to stay dry. Should i walk or run in the rain?
- A man has three daughters. A second, intelligent man, asked him the ages of his daughters. The first man told him that the product of their ages (them all multiplied together,) was 36. After thinking the second man was unable to find the answer and asked for another clue. The first man replies the sum of their ages is equal to his house door number. Still the second man was unable to answer and asked for another clue. The first man told him that his youngest daughter had blue eyes, and suddenly second man gave the correct answer. Explain how?
- A regular clock has an hour and minute hand. At 12 midnight the hands are exactly aligned. When is the next time they will exactly align or overlap?
- You are in a dark room with a deck of cards. N of the cards are face up and the rest are face down. You can't see the cards. How do you divide the deck in to two piles with equal numbers of face up cards in each?
- If an aeroplane makes a round trip and a wind is blowing, is the trip time shorter, longer or the same?
- On a deserted road, the probability of observing a car during a thirty-minute period is 95%. What is the chance of observing a car in a ten-minute period?
© Nigel Coldwell 2013 - The questions on this site may be reproduced without further permission, I do not claim copyright over them. The answers are mine and may not be reproduced without my expressed prior consent. Please enquire using the link at the top of the page.
arrogant to add a donate button, but i've had as
many as 1 emails requesting it. Don't feel you have to but if you want
to then as little as £1 would pay for hosting for nearly a
week. - nigel