Motto

The one who does no stupid thing, is not as clever as he thinks.

Babler

Math Brain Teasers

Brick

An old riddle is as follows: One brick is one kilogram and half a brick heavy.
What is the weight of one brick?
(This is a typical elementary math brain teaser.)

Solution

Strange Coins

I have two US coins totaling 55 cents. One is not a nickel.
What are the coins?

Solution

What is Correct

Is it correct that seven and five is thirteen or seven and five are thirteen?

Solution

Trains

A train leaves New York for Boston. Five minutes later another train leaves Boston for New York, at double the speed.
Which train will be closer to New York when they encounter?

Solution

Fly

Two trains 200 km from each other are moving at the speed of 50 km/hour towards each other. From one train a fly takes off (at the moment the trains are 200 km from each other), flying straight (upon the rails) to the other train at the speed of 75 km/hour, bounces away from it and flies back to the first train. This is repeated till the trains crash into each other and the fly is smashed.
What distance is the fly able to fly until its death?
(There is a complicated and an easy way to solve this math brain teaser.)

Solution

Speeding up

If I go halfway to the town (which is 60 km away) at the speed of 30 km/hour, how fast do I have to go for the rest of the way to have the average speed of the entire way 60 km/hour?
(Hint: "rest of the way" means to the town and not an inch farther and the total distance traveled has to be exactly 60 km - this is just to explain how I meant the riddle to be understood.)

Solution

Wired Equator

The circumference of the globe is approximately 40,000 km. If we made a circle of wire around the globe, that is only 10 metres (so 0.01 km) longer than the circumference of earth, could a flea, a rabbit or even a man creep under it?

Solution

Diophantus

We know little about this Helen mathematician from Alexandria (called the father of algebra) except that he lived about the year 250 B. C. Due to one admirer of his, who described his life by the means of an algebraic riddle (math brain teaser), we know at least something about his life.
Diophantus's youth lasted 1/6 of his life. He had his first beard in the next 1/12 of his life. At the end of the following 1/7 of his life Diophantus got married. Five years from then his son was born. His son lived exactly 1/2 of Diophantus's life. Diophantus died 4 years after the death of his son.
How long did Diophantus live?

Solution

Ahmes's Papyrus

About 2000 B. C. there lived Ahmes, a royal secretary and mathematician of the Pharaoh Amenemhat III. In 1853 an Englishman Rhind found one of Ahmes's papyruses near the temple of Ramses II. in Thebes. The papyrus is a rectangle 33 cm wide and about 5 m long. There is the following math brain teaser on it (besides others).
100 measures of corn must be divided among 5 workers, so that the second worker gets as many measures more than the first worker, as the third gets more than the second, the fourth more than the third and the fifth more than the fourth. The first two workers shall get seven times less measures of corn than the three others.
How many measures of corn shall each worker get?

Solution

Midnight

If it were two hours later, it would be half as long until midnight as it would be if it were an hour later.
What time is it now?

Solution

Clock

On every clock we can see that at noon the hour, minute and second hand correctly overlay. In about one hour and five minutes the minute and hour hand will overlay again.
What is the exact time (to a millisecond) when it will occur and what angle will they form with second hand?
(Assume that the clock hands move continuously.)

Solution

Reservoir

One reservoir has four taps. Using the first takes two days to saturate the reservoir, the second tap three days, the third four days and the last one 6 hours.
How long will it take to fill the reservoir using all 4 taps at once?

Solution

Car

A military car carrying an important letter must cross a desert. There is no petrol station on the desert and the car has space only for petrol that lasts to the middle of the desert. There are also other cars that can transfer their petrol to one another.
How can the letter be delivered?

Solution

Aeroplane

There is only one airport on a fictional planet, and that is on the north pole. There are only 3 aeroplanes and lots of fuel at the airport. A full tank of an aeroplane lasts exactly to the south pole, however the aeroplanes can transfer their fuel to one another.
Your mission is to fly round the globe with at least one aeroplane (above the south pole) and in the end all aeroplanes must return to the airport.

Solution

Belt

A magic rectangular belt always shrinks its length to 1/2 and width to 1/3 whenever its owner wishes something. After three such wishes, its surface was 4 cm².
What was the original length, if the original width was 9 cm?

Solution

Baldyville

These are the conditions in Baldyville:

No two inhabitants have the same number of hairs on their head.
No inhabitant has exactly 518 hairs.
There are more inhabitants than any inhabitant's hair in the town.

What is the highest possible number of inhabitants?

Solution

Josephine

The recent expedition to the lost city of Atlantis discovered scrolls attributed to the great poet, scholar, philosopher Josephine. They number eight in all, and here is the first.
The kingdom of Mamajorca, was ruled by queen Henrietta I. In Mamajorca women have to pass an extensive logic exam before they are allowed to get married. Queens do not have to take this exam. All the women in Mamajorca are loyal to their queen and do whatever she tells them to. The queens of Mamajorca are truthful. All shots fired in Mamajorca can be heard in every house. All above facts are known to be common knowledge.
Henrietta was worried about the infidelity of the married men in Mamajorca. She summoned all the wives to the town square, and made the following announcement. "There is at least one unfaithful husband in Mamajorca. All wives know which husbands are unfaithful, but have no knowledge about the fidelity of their own husband. You are forbidden to discuss your husband's faithfulness with any other woman. If you discover that your husband is unfaithful, you must shoot him at precisely midnight of the day you find that out."
Thirty-nine silent nights followed the queen's announcement. On the fortieth night, shots were heard. Queen Henrietta I is revered in Mamajorcan history.

Solution

Why 1 = 2

Where is the mistake in these mathematical equations?

x = 2
x(x-1) = 2(x-1)
x2-x = 2x-2
x2-2x = x-2    
x(x-2) = x-2    
x = 1

Solution

Open polygon

Join all 9 dots creating an open polygon with four lines.

Solution

Do you know an interesting puzzle? One that you really like or one that you don't know solution to? Share it with the world - post it as new topic into my New Puzzles Forum.