Split the Cube
Can a cube be split into smaller cubes, all with different sizes?
SOLUTION
Solution coming soon.
Unknown Author
We do not know where this puzzle originated from. If you have any information, please let us know via email.
We do not know where this puzzle originated from. If you have any information, please let us know via email.
Airplane on a Conveyor Belt
A Boing 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Will the plane take off?
SOLUTION
Solution coming soon.
Had Had Had Had Had
A teacher in English had asked James and John to describe a man who had suffered from a cold in the past. James while John had had had had had had had had had had had a better effect on the teacher.
Add punctuation to the sentence in bold, so that it makes sense.
SOLUTION
A teacher in English had asked James and John to describe a man who had suffered from a cold in the past. James, while John had had “had”, had had “had had”; “had had” had had a better effect on the teacher.
The meaning is that John had used the phrase “had a cold”, whereas James had used the phrase “had had a cold”. The former, being more grammatical, had resulted in a better impression on the teacher.
Average Salary
Three friends, A, B and C, want to find out what their average salary is without disclosing their own salaries to the others. How can they do it using only verbal communication?
SOLUTION
A tells B some number, then B adds his salary to it and tells the result to C, then C adds his salary and tells the result to A. Now A subtracts the number he told B in the beginning, adds his own salary and divides by 3. Repeat the same procedure with B and C starting first.
Eminent King
Five hundred begins it,
five hundred ends it,
five in the middle is seen.
The first of all letters,
the first of all numbers
take up their stations between.
Put them all together
and bring before you
the name of an eminent king.
SOLUTION
The answer is DAVID. In Roman numerals D=500, V=5, I=1.
Six Glasses
Six identical glasses are placed in a row on the table – first three filled with water, and then three empty ones. Can you move just one glass, so that empty and full glasses alternate?
SOLUTION
Take the second full glass, pour all the water into the second empty glass, and then put it back in its place.
Protect the Treasure
Nine pirates have captured a treasure chest. In order to protect it, they decide to lock it using multiple locks and distribute several keys for each of these locks among them, so that the chest can be opened only by a majority of the pirates. What is the minimum number of keys each of the pirates should get?
SOLUTION
First, we show that for every four pirates, there exists a lock which cannot be opened only by them and can be opened by everyone else. We choose an arbitrary group of four pirates. If they can open every lock, then they can access the treasure without the need of a majority. If any of the remaining pirates cannot open that lock, then he, together with the initial group of four still cannot access the treasure. Thus, the claim is proved and to each group of four pirates we can assign a unique lock. These are \binom{9}{4}=126 locks in total. Finally, every pirate should get keys for \binom{8}{4}=70 of these locks, one for each group of four additional pirates he can be a group of.
Buried Up to Neck
Three friends, Adam, Bob, and Charlie are buried in the sand up to their necks, all facing West. Charlie can see both Adam and Bom, Bom can see only Adam, and Adam cannot see anyone. Black and white hats are placed on their heads. The three friends are told that there is at least one hat from each color, and then they are asked whether anyone can guess the color of their own hat.
After a few minutes, one of them answers. Who is that?
SOLUTION
If Adam and Bob had hats with identical colors, then Charlie would immediately be able to deduce that his hat has the opposite color. Charlie doesn’t do that, so Adam and Bob are able to figure out that their hats have opposite colors. Since Bob is the one who can see the color of Adam’s hat, he is the one that answers the question.
The Letter E
Click the image to enlarge it and download it. Then print it, cut out the three pieces, and rearrange them so that you get the letter “E”.
SOLUTION
Rearrange the pieces, so that they form the shadow of the letter “E”, as shown below.
Fish Eat Fish
A hundred fish are swimming along a stream at different velocities. If one fish catches up to another fish, it eats it and continues swimming. What is the expected number of fish that will survive?
SOLUTION
Notice that the N-th fish in the stream survives if and only if it is the fastest among the first N fish. The probability of this event happening is equal to 1/N. Since the expected number of fish that survive is equal to the sum of the survival probabilities for each of them, the answer is 1+1/2+1/3+…+1/N.
For more details on the last claim, consider reading our blog post “How Many Times on Average?”