CausalPaths

A N A L Y T I C S

Quantnotes.com · Edutainment Archive

Easy Brain Teasers

Logic, arithmetic, and classic lateral-thinking puzzles.

15 puzzles recovered from the original Quantnotes.com Edutainment section (c. 2001–2008). Click a title to read the puzzle, then press Show Answer to reveal the solution.

01 The Age Problem

Jamie is 24 years old. Jamie is twice as old as Jill was when Jamie was
as old as Jill is now.
How old is Jill now?

Show Answer ▾

18 years old

02 The Appointment

John had an appointment in London at two o'clock in the afternoon. If
he left his home and travelled at 15 km/h, he would arrive at one o'clock.
If he travelled at 10 km/h, he would not arrive until three o'clock.
What is the distance from his home to London?

Show Answer ▾

60 km, he left home at 9 a.m.

03 Burning Candles

You have 2 candles of same height but of different widths. One takes
4 hours to burn all the way while the other takes 7 hours. Assuming they
burn at steady rates, how long will it take before one candle is twice
as tall as the other?

Show Answer ▾

2 hours 48 minutes.
Say the initial height of the candles is h, the burn rates
are h/4 and h/7 respectively.
After time t, the heights of both candles are (h - h/4
* t) and (h - h/7 * t) respectively. We know that
2 * (h - h/4 * t) = (h - h/7 * t)
Therefore
t = 2.8 hours or 2 hours 48 minutes
This is too easy...

04 Car Hire Problem

John hired a car at a cost of £15 per day to take him to Oxford
and back again in the evening. When he got halfway on his outward journey
he met a friend, gave him a lift to the town and brought him back to the
point where he picked him up in the morning.
There is a dispute about the payment. How much should John charge his
passenger for his share of the motor hire?

Show Answer ▾

5 pounds.

05 Family Ties

In 1992, a father's age added to that of his wife was ten times the sum
of the ages of their children. In 1994, it was only six times the sum,
and in 2000 it had fallen to three times the sum.
How many childrens have they (They are all alive)?

Show Answer ▾

3.

06 The Fly and the Cyclists

Two cyclists 20 km apart start at the same instant and ride towards each
other along a straight road at a speed of 10 km/h. At the same instant
a fly on the forehead of one of the riders starts to fly at 15 km/h towards
the other rider, alights on his forehead and then flies back to the first
rider.
The fly travels back and forth over the continuously decreasing distance
between the two riders until it is finally squashed as the foreheads of
the two riders meet. How far has the fly flown when all his journeys are
added together?

Show Answer ▾

15 km.

07 Freedom or Execution

You are a prisoner but are a given a chance to escape. There are two
guarded doors, behind one freedom, behind the other execution! One guard
always lies and the other always tells the truth. You are allowed one
question. What would you ask?

Show Answer ▾

A valid question would be 'Will the other
guard say that this door leads to execution?' If any of the guards is
standing in front of the execution door they will say 'no', and they'll
say 'yes' if they're standing in front of the freedom door. Another valid
question is 'Is the truthful guard standing in front of the execution
door?' In this case, if any of the guards is standing in front of the
execution door they'll say 'yes' and in front of the freedom door they'll
say 'no'. The question has got to relate the guards and the doors.

08 The Journey

If the journey between London and Manchester takes four and a half hours
and vice versa, and that a train starts from each city every hour on the
hour.
How many trains from Manchester will a passenger from London to Manchester
meet and pass on the journey?

Show Answer ▾

9 trains.

09 Just Whisky

A friend of yours has just bought a big container of whisky: 12 litres.
He decides to share it with you only if you can divide it exactly evenly:
6 litres each. The problem is that you only have with you a 5 and an 8
litres container. How can you do it?

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Fill the 8 liter container and use it to fill
the 5 liter container. Pour the last back into the 12 liter container.
Pour the 3 liters left in the 8 liter container into the now empty 5 liter
container. Use remaining 9 liters to fill the 8 liter container. Use this
to top up the 5 liter container, and thus leaving 6 liters in the 8 liter
container. Empty the 5 liters back into the 12 liter container which contains
1 liter.

10 Skinned Cube

You have a 10 x 10 x 10 cm^3 cube made up of individual 1 x 1 x 1 cm^3.
The outer surface of the cube is removed. How many cubes are removed?

Show Answer ▾

This is a very easy problem the actual answer
of which is besides the point. Most people presented with is problem immediately
start thinking in terms of surface areas of the faces removed. The smarter
minority see that the inner cube left is an 8 x 8 x 8 cm^3 cube. Therefore,
we have removed 10^3 - 8^3 cubes.
This question is designed to demonstrate how sometimes
problems are unnecasserily complicated depending upon how it is viewed.

11 Selling Eggs

In a market, a woman sold to Mr. Jones half her stock of eggs and half
an egg. She then sold to Smith half of her remaining stock and half an
egg. Then Robinson bought half of the eggs which she had left and half
an egg. Finally Brown then bought the rest of her stock, thirty-three
eggs in total.
How many eggs did she have to start with? She did not sell any broken
eggs.

Show Answer ▾

271 eggs.

12 Sun Dried Tomatoes

You have 1000 kilograms of tomatoes. The tomatoes are 99% water. You
want to sell sun dried tomatoes. After a day of drying water makes up
for 98% of the tomatoes. How much do they weigh now?

Show Answer ▾

Initially the tomato is made of 1% dry mass, that
is 10 kg. After drying, the dry mass instead of representing 1 % actually
represents 2. The question becomes: if 2% is 10 kg how much is the total?
It is of course 50 x 10kg = 500 kg. Half of the initial weight! Although
almost 50 % of the water evaporated it still represents 98% of the tomatoes.

13 The Explorers

Four explorers make a journey into the desert. Each man carries enough
food to last him five days. After the party has gone some distance, one
man starts turning back, taking him just enough food to last him until he gets
back to his starting point. Then a second man does so likewise, and so on.
How many days' journey can the last man make into the desert and return
safely? It is assumed that food can be transferred from person to person,
and that each man travels in units of full days.

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4 days out and 4 days back, 8 days in total.

14 Whiskey and Water

One tank is half full of water, and another half full of whiskey. A spoonful
of water is taken from the first tank and mixed with the whiskey in the
second. A spoonful of the watered whiskey is then taken and mixed in the
tank of water. Is the amount of water taken from the first tank greater
or less than the amount of whiskey taken from the second tank?

Show Answer ▾

the same.

15 Wounded Soldiers

Four soldiers, of which three are wounded, need to cross a dangerous
bridge at night time to escape their enemy. The bridge can support at
most two soldiers at any one time. The soldiers have only one torch light
which needs to be used during the crossing. The non wounded soldier can
cross the bridge in 1 minute, whilst the less lucky ones take 2, 5 and
10 mintues respetively. Whilst crossing the bridge the less wounded soldier
would need to support his buddy, and thus cross the brige at his buddy's
pace.
What is the shortest time they can reach the other side in?

Show Answer ▾

17 min. Start by sending the less wounded soldier
with the non wounded one (2min). Send the healthy one back (1min). Send
the two badly wounded ones together (10min). Then let the less wounded
soldier return with the torch to collect the healthy one (2+2 min).