Begin the Beguine, Ella Fitzgerald
Part of Torsten Johanssons site
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| BRAIN TEASERS |
Can you solve these problems?
For some of the problems are given answers at the end of the page
Problems number 13, 14, 15 are added the 28th of March 2003
1. THE BALANCE AND THE TWELVE MARBLES
You have twelve numbered, apparently identical, marbles.
Everyone - except one - has the same weight. You don't know
which marble has a different weight. Nor do you know whether
it weighs more or less than the rest.
By using the balance no more than three times you should
be able to identify the odd marble and also indicate whether
it is heavier or lighter than the remaining marbles.
Click here if you want to download
The Balance Game.
You can play the game off line.
You can change between Swedish and English by clicking on the flag.
When you have got it, read the text and click on it
and you will have the balance on the screen
2. ARITHMETICAL EXERCISE
Try to find a number which is the sum of all the numbers
by which it is divisible (with no remainder).
3. PLENTY OF POULTRY
The carpenter's wife buys poultry in the market. She can take her pick
from ducks, hens and geese. Having finished her purchases, she has spent
exactly 100 crowns and is able to take home all three varieties, 100 birds
altogether. She has paid 50 ores for a duck, 3 crowns for a hen, and for
a goose 10 crowns.
How many birds of each kind has she bought?
(1 crown is divided into 100 ores)
4. DON'T SHUFFLE YOUR DECK
There are four playing-cards in a deck
On top of an ace is an ace
On top of a heart is a spade
Under an ace is a king
Under a diamond is a heart
On top of diamond is a heart
Under a king is an ace
What are the four cards?
5. THE RIVER, THE BRIDGE, AND THE SOLDIERS
Four wounded soldiers are trapped in hostile country. Hiding on the
wrong side of the border river, they want to escape to their neighbouring
homeland. The only way to get across is by an ill-repaired bridge, which
will only hold two soldiers at a time. Moreover, the bridge is mined and
it's night-time so those who want to go across will have to use a torch
in order to be able to miss the mines. Unfortunately, the soldiers have
only one torch between them.
Since the soldiers suffer wounds of different degrees, their crossing times are as follows:
Private Jones: 5 minutes
Private Harris: 10 minutes
Private Brown: 20 minutes
Private Evans: 25 minutes
The enemy is within an hour of the soldiers. Can they
make the crossing before the time runs out? In which order
must the pairs go across? (Remember that the torch will
have to be carried at all times!)
6. THE STONE MARBLES
Andrew is given ten large bags of stone marbles. His father tells
him that each marble in one of the bags weighs three grammes less
than each of the marbles in the rest of the bags. The heavier marbles
weigh 20 grammes each. Andrew gets to keep all marbles if he is able
to identify the bag containing the lighter marbles. He is allowed one
weighing session only on a balance with a gramme scale. Andrew was
able to solve the problem. Are you?
7. THE WOLF, THE GOAT AND THE CABBAGE
Here is a truly classic problem:
A man is about to cross a stream in a rowing-boat. He is carrying a wolf
a goat an a head of cabbage. He can´t bring with him more than one of
his objects in one crossing. The wolf can´t be left alone with the goat
and the goat can´t be trusted on its own with the cabbage. - How can the
man handle the situation to put everyone and everything safely on the
other side of the stream?
8. RUNNING AND DRAINING THE BATH
Let´s suppose your bath-tub can be filled right to the edge through the
hot water tap in 8 minutes. Instead, by running cold water the tub
would fill in 6 minutes. Once the tub is filled right up, it will take
4 minutes to drain.
If all taps and the drain are open, will the tub ever fill up?
And if it will, how long will it take?
9. BACHET's WEIGHTS PROBLEM
What is the least number of weights that can be used on a scale
pan to weigh any integral number of pounds from 1 to 40 inclusive,
if the weights can be placed in either of the scale pans?
10.
WATER BARRELS
In the first instance there are three barrels (A, B, and C),
all of them containing differing amounts of water.
By pouring water from A to B and C, the volumes of B and C
are both doubled.
Water is then poured from B to A and C, doubling the volumes of A and C.
At last water is poured from C to A and B, again doubling
the volume of A and B.
How much water did each barrel hold in the beginning, knowing
that each barrel in the end contained 24 litres each?
11.
THE SOLDIER AND HIS ANIMALS
Private Jones has lost a leg in the war. His lost leg has
been replaced by a wooden one. He has retired to the
countryside where he breeds chickens and rabbits.
Private Jones gets the question how many animals he has.
He answers: "there are 25 of us all in all - chickens, rabbits and
myself - and on average we have three legs each."
How many chickens and rabbits does Private Jones own?
12.
EXAM IN HISTORY
A group of students sits a written exam in history. Their task is
to pair four historical events with four dates. Their result is
as follows:
- 25 per cent have answered all questions correctly
- 10 per cent have answered all questions incorrectly
- 36 students have answered two questions correctly
- 5 per cent have answered one question correctly
How many students sat the exam?
13. THE PROFESSORS’ HATS
Three professors sit on a chair each, one behind the other, and all
three facing the same direction. They are given a hat each from a bag
originally containing two black hats and three white ones.
None of the professors can see their own hat. The one sitting furthest
back can see the hats worn by the two in front. The one sitting in the
middle can only see the one at the front. The one sitting at the front
can’t see the hats behind him.
The professors are instructed to shout the colour of their own hat
the moment they know it. Suppose you are the professor sitting at
the front and that both other professors remain silent. After a while
you realise what colour your hat is.
What is the colour of your hat and how did you come to this conclusion?
14. MONEY TROUBLE
A man has 25 bills made up of five- and ten-dollar bills. If he were
to exchange one of the tens for two fives, he would then have as many
tens as fives.
How much money did the man have in his wallet?
15. WHO OWNS THE GOLDFISH?
In a street there are five houses in a row. They all have different
colours. The owners of the houses are all different nationalities.
All owners have different drink preferences, smoke cigarettes of
different brands and have different kinds of pets.
Who owns the goldfish?
Facts:
The Englishman lives in the red house.
The Swede owns a dog.
The Dane drinks tea.
The green house is to the left of the white one.
The owner of the green house drinks coffee.
The person smoking Pall Mall breeds birds.
The owner of the yellow house smokes Dunhill.
The person living in the middle house drinks milk.
The Norwegian lives in the house furthest to the left.
The person smoking Blend lives next to the cat owner.
The horse owner lives next to the Dunhill smoker.
The person smoking Bluemasters drinks beer.
The German smokes Prince.
The Norwegian lives next to the blue house.
The person smoking Blend has a next-door neighbour who drinks water.
It’s rumoured that Einstein thought up this problem and stated that
98 per cent of the world’s population wouldn’t be able to solve it.
16. THE WORLDS FIRST PALINDROME
Who created, or uttered, the world´s first palindrome?
A palindrome is a sequence of letters that will spell
the same sentence, or message, whether read forwards
or backwards.
17. HOW MANY COWS AND HOW MANY GEESE?
20 animals live in Lisa's barn. All in all, the animals have a total of 62 legs.
The only animals that live there are cows and geese.
How many cows and how many geese live in Lisa's barn?
18. HOW MANY MICE? (MICE AND LICE)
If six mice eat six lice in six minutes, how many mice must there be
to manage to eat 100 lice in 100 minutes?
Do you need hints or answers?
Hint: It might prove a good idea to place a Answer:
For example: 28 (1+2+4+7+14)
Answer: 5 geese at 10 crowns=50 crowns, 1 hen at 3 crowns=3 crowns,
94 ducks at 50 ores=47 crowns.
Two answers:
To minimize time consumption:
Answer:
To provide an answer to this problem would entirely rob the
The tub is filled after 24 minutes.
If none of the weights must be placed in the same scale pan as the object being weighed,
Answer:
Barrel A 39 litres, barrel B 21 litres, barrel C 12 litres
Answer: 11 chickens and 13 rabbits
Answer: 60 students
Let’s name the professors A, B and C. - A sits at the front, B in the
middle and C at the back.
A must ask himself why neither of the other two shout the colour of
their hats.
He can conclude that the only condition allowing C certainty would be if
If B, after having observed the fact that C is silent,
The fact that B and C remain silent makes A certain he’s wearing a white
hat.
Correct answer: The German owns the goldfish.
If you will have the green house directly to the left
The correct answer is ADAM.
If there are X mice they will eat X * 100/6 lice in the stipulated time and that number should be 100 lice.
The equation: X * 100/6 = 100. Thus X = 6. Answer: there must be 6 mice.
Back to the problems, formulated above
Return to index page!
The translation into English was made by my son Claes Swedenborg.
number of marbles other than six in each of the pans. Try to decide what
the causes could be for each of the three possible results of each weighing
session! Do this after each session! Make clear you understand what conclusions
must be drawn from each outcome. These conclusions will decide how you
need to arrange the next weighing. It will take some time to go through
all steps of thought and to remember what the previous ones were. Therefore,
it's a good idea to use a pen and paper. You could also develop some kind
of flow chart, aiding your thought.
2. ARITHMETICAL EXERCISE
3. PLENTY OF POULTRY
4. DON'T SHUFFLE YOUR DECK
from the top:
a) King of Spades - Ace of Hearts - Ace of Diamonds - King of Hearts
b) Ace of Spades - King of Hearts - Ace of Diamonds - Ace of Hearts
5. THE RIVER, THE BRIDGE, THE SOLDIERS
a) slow soldiers should cross together (only one
crossing must take a long time)
b) faster soldiers make the return trip
Passage and direction
Time consumption
1. Homeward: Pte Jones+Pte Harris
10 mins.
2. Return: Pte Jones
5 mins.
3. Homeward: Pte Brown+Pte Evans
25 mins.
4. Return: Pte Harris
10 mins.
5. Homeward: Pte Jones+Pte Harris
10 mins.
Total time:
60 mins.
6. THE STONE MARBLES
problem-solver of the satisfying aha-experience which will be had
when hitting up the correct solution - so I do´nt.7. THE WOLF, THE GOAT AND THE CABBAGE
1. The goat is rowed across. The man returns singlehanden.
2. The head of cabbage is rowed across. The man returns
accompanied by the goat.
3. The wolf is rowed across. The man returns singlehanden.
4. The goat is rowed across, bringing the problem to its solution. 8. RUNNING AND DRAINING THE BATH
9. BACHET's WEIGHTS PROBLEM
Four weights of 1, 3, 9 and 27 pounds are required. Using only these four weights
can be accomplished if one or more of the weights are placed in the same scale pan
as the object being weighed.
six weights are required; 1, 2, 4, 8, 16 and 32 pounds.10. WATER BARRELS
11. THE SOLDIER AND HIS ANIMALS
12. EXAM IN HISTORY
13. THE PROFESSORS´HATS
C could see two black hats. C must, since he doesn’t shout, see either
two white hats or one white and one black hat.
sees a black hat on A, he must then conclude that he’s wearing a white
hat. For him to remain uncertain and silent A must wear a white hat. 14. MONEY TROUBLE
Correct answer: The man had 195 dollars.
15. WHO OWNS THE GOLDFISH?
Colour
Green
Blue
Red
Yellow
White
Nationality
Norwegian
German
Englishman
Danish
Swedish
Beverage
Coffee
Water
Milk
Tea
Beer
Animals
Bird
Fish
Horse
Cat
Dog
Cigarette
Pall Mall
Prince
Blend
Dunhill
Bluemasters
of the white house
the correct answer still is the same: The German owns the goldfish
Colour
Yellow
Blue
Red
Green
White
Nationality
Norwegian
Danish
Englishman
German
Swedish
Beverage
Water
Tea
Milk
Coffee
Beer
Animals
Cat
Horse
Bird
Fish
Dog
Cigarette
Dunhill
Blend
Pall Mall
Prince
Bluemasters
16. THE WORLDS FIRST PALINDROME
When Adam saw Eve for the first time he said
Madam I´m Adam 17. HOW MANY COWS AND HOW MANY GEESE?
Answer: 11 cows and 9 geese
18. HOW MANY MICE?
A mouse needs 6 minutes to eat one louse so in 100 minutes a mouse can eat 100/6 mice.
Thank you very much, Claes!