Brain-Teasers
i. Fun with Fuses...
Assume, you have a number of long fuses, of which you only know that they burn for exactly one hour after you lighted them at one end. However, you don't know whether they burn with constant speed, so the first half of the fuse can be burned in only ten minutes while the rest takes the other fifty minutes to burn completely. Also assume that you have a lighter.The Question: How can you measure exactly three quarters of an hour in time with these fuses?
ii. Alien Alert...
There are three Federation Officers assigned to take three hostile aliens to "Peace Talks" on another planet. However, they must follow the following rules:- They have only one small space ship.
- Only two individuals can ride in the space ship each time.
- All Federation Officers can pilot the space ship, but only one alien can pilot the ship.
- There must always be more (or the same number of) Federal Offices than aliens on any of the planets, because if there are more aliens than Federation Officers then the aliens will kill the Federation Officers. Count any individual in the space ship when it is on one planet as being on that planet.
- The one space ship is the only means of transportation. There is no other way to get to the "Peace Talks". No one can exit the space ship while it is in flight.
- To start off, all the Federation Officers and aliens are on the same planet.
The Question: Can all Federation Officers and aliens get to the other planet alive, and if so: how?
iii. A Quiz...
You are a participant in a quiz. The quizmaster shows you three closed doors. He tells you that behind one of these doors there is a prize, and behind the other two doors there's nothing. You select one of the doors, but before you open it the quizmaster contiously picks out a remaining empty door and shows that there is nothing behind it. The quizmaster offers you a chance to switch doors with the remaining closed door.The Question: Should you stick to your choice?
iv. Troubled Traveler
A traveler, on his way to a certain village A, reaches a road junction, where he can turn left or right. He knows that only one of the two roads leads to village A, but unfortunately, he does not know which one. Fortunately, he sees two twin-brothers standing at the road junction, and he decides to ask them for directions.The traveler knows that one of the two brothers always tells the truth and the other one always lies. Unfortunately, he does not know which one always tells the truth and which one always lies.
The Question: How can the traveler find out the way to village A by asking just one question to one of the two brothers?
v. John & Julia
Julia is as old as John will be when Julia is twice as old as John was when Julia's age was half the sum of their present ages.John is as old as Julia was when John was half the age he will be 10 years from now.
The Question: How old are John and Julia?
vi. Square Puzzle
The five pieces shown below must be put together to a square.![[Five Pieces]](fivepcs.gif)
The Question: How should this be done?
A Hint: Print the picture with the pieces, and cut the pieces out. It's more difficult than it looks!...
vii. 3 Heads & 5 Hats
In a small village in the middle of nowhere, three innocent prisoners are sitting in a jail. One day, the cruel jailer takes them out and places them in a line on three chairs, in such a way that man C can see both man A and man B, man B can see only man A, and man A can see none of the other men. The jailer shows them 5 hats, 2 of which are black and 3 of which are white. After this, he blindfolds the men, places one hat on each of their heads, and removes the blindfolds again. The jailer tells his three prisoners that if one of them is able to determine the color of his hat within one minute, all of them are released. Otherwise, they will all be shot. None of the prisoners can see his own hat, and all are intelligent. After 59 seconds, man A shouts out the (correct) color of his hat!The Question: What is the color of man A's hat, and how does he know?
viii. Missing Man
Look at the figure below, which shows fifteen men. The figure is subdivided into three areas (upper left, upper right, and the bottom half).
By exchanging the upper two parts of the figure, one gets the figure below. This new figure however only shows fourteen men! (If you don't belief what happened here: please print it, cut it, and try it out yourself!)
The Question: Where did the missing man go?
ix. Colourful Dwarfs
In a distant, dark forest, lives a population of 400 highly intelligent dwarfs. The dwarfs all look exactly alike, but only differ in the fact that they are wearing either a red OR a blue hat. There are 200 dwarfs with a red hat and 200 dwarfs with a blue hat. Striking however, is that the dwarfs don't know these numbers themselves and that none of them knows what the colour of his hat is (there are for example no mirrors in this forest).During a certain period of their year, there is a big party in this village, to which initially all dwarfs will go. However, this party is only intended for dwarfs wearing a blue hat. Dwarfs with a red hat are supposed never to return to the party again, as soon as they know that they are wearing a red hat.
The Question: How many days does it take before there are no more dwarfs with a red hat left at the party?
![[Pirates!]](pirate.gif)
x. Pirate Treasure
A pirate ship captures a treasure of 1000 golden coins. The treasure has to be split among the 5 pirates: 1, 2, 3, 4, and 5 in order of rank. The pirates have the following important characteristics:
Infinitely smart.
Bloodthirsty.
Greedy.
The Question: What proposal should pirate 5 make?
xi. Bizarre Boxes
Someone shows you two boxes and he tells you that one of these boxes contains two times as much as the other one, but he does not tell you which one this is. He lets you choose one of these boxes, and opens it. It turns out to be filled with $10. Now he gives you the opportunity to choose for the other box in stead of the current one (and skip the $10 of the first box), because the second box could contain twice as much (i.e. $20).The Question: Should you choose for the second box, or should you stick at your first choice to maximize the expected amount of money?
A Hint: If you have $10, and you could double this with a chance of 1/2, or half it with a chance of 1/2, one would expect an average of 1/2 * $20 + 1/2 * $5 = $12.5 (so you would expect to gain $2.5)!...