Mathematical puzzles

Puzzles, situation puzzles and recreational mathematics.

situation puzzles and recreational mathematics. Neuron juice

Neuron juice.

The important thing is not to stop questioning. (Albert Einstein.)

Math Puzzles

In this site you can find a selection of the most popular riddles and situation puzzles. Obviously, neither are here all who matter nor they matter all who are here. Some of them have been taken from the missing Snark list; others from books and other have been on my mind for a long time.


Every suggestion will be appreciated and included in this list.


Two of the riddles deserve special treatment, The riddle of the ages and the piano student is the one I always propose as a challenge. The other one is "Einstein's puzzle"  —if you don't know it yet, I highly recommend it.


Riddles and situation puzzles are mixed because of the difficulty of dividing them correctly into two independent groups, as some of them could be included in both groups.




12.- A milkman has a jug of 8 liters full of milk, and two more of 5 and 3 liters.

A customer asks for exactly 4 liters.

How can he calculate 4 liters and give it to the customer in the 5-liter jug?


-- Solution of the riddle --



Sent by Xavier Cases Camats.

11.- The warden of a prison lets know that he will release somebody randomly to celebrate he has been warden for 25 years.

A man is chosen and told he will be released if he takes a white ball from a box, where there are 9 black ones and just 1 white ball.

The prisoner knows thanks to a tip-off that the warden will make all the balls be black. The next day, the game takes place and the prisoner is released.

How could he get out of prison if every ball is black?


-- Solution of the riddle --




10.- A survey taker goes to a house where he questions a woman:

Number of children? Three, she answers.

Ages? The product of their ages is 36 and the addition is the same as the number of this house.

The survey taker leaves but later he comes back and tells the woman that the information provided is not enough. The woman thinks and says: You are right, the older one studies piano.

This is enough for the survey taker to guess the children's age. What are their ages?






9.- Three friends in difficulties share a cup of coffee that costs 30 cents, so each one of them puts 10 in.

When paying they ask for a discount and the owner reduces the price in 5 cents so each one of them takes one cent and keep 2 in a common fund.

Later they do the numbers and they say:

Each one has paid 9 cents so we have spent 9x3=27 cents, plus the 2 in the fund equals 29.

Where is the missing cent?





Riddle. 8.- This riddle is mainly the same as the previous one about the twelve coins, but now we don't know if the different coin is heavier or lighter than the others, and we have just three tries.

The question is which is the different coin and wheter it is heavier or lighter.





Riddle. 7

We have twelve coins that look similar, but one of them is slightly heavier.

Using a pan balance and just three tries, find the different coin.





Riddle. 6.- A prisoner is locked up in a cell that has two doors —one leads to death and the other one to freedom.

Each door is guarded by a watchman.

The prisoner knows that one of them always tells the truth and the other one always lies.

To choose the door, he can just ask a question to a watchman.

How can he save himself?






Riddle. 5.- On a table there are three black hats and two white ones.

Three men in a straight line put on a hat each one randomly and without knowing its colour.

The third one in the line, who can see the other ones' colour, is asked if he can tell his hat's colour —he says no.

The second one, who can only see the first one's hat, is asked the same question but can't tell his colour.

Finally, the first one, who can see no hat, tells correctly the colour of his hat.

Which is his colour and how could he know it?





Riddle. 4.- A man is at the beginning of a long hallway that has three switches; at the end of the hallway there is a room with a closed door.

One of the switches turns on the light of the room, which is turned off.

How could he know which switch turns on the light if he just went through the hallway once?

Hint: The man has a flashlight.





2.- A bear walks 10 km. to the South, 10 to the East and 10 to the North, going back to the place where it started. What is the colour of the bear?