Riddles!

(Note: All are solvable, though some may be hard)

Riddle 1:

You are Alice in wonderland, and you must go through a hedge maze in order to arrive at the Queen's Palace. However it is terribly dark and you can't see anything, also you haven't got anything you could use to mark your way through the maze. How could you go to the other side? (Assuming of course, the maze is solvable). If you already know the answer (some people do) try to prove why it solves the riddle, and what is the crucial detail which without it, the riddle can not be solved? (Solution)

Riddle 2:

You walk into a dark room in which one hundred coins are scattered around on the floor. You are told that ten of them have "heads" on top, and that ninety have "tails". Your mission is to separate the coins into two groups such that the amount of coins showing "heads" are equal in each group. You can not see, feel, smell, taste or hear on which side the coins are. Can you perform the mission in a way that it will always work?

Riddle 3:

Three men are invited to participate in a game. They receive hats in the colours of Red and Blue, and the colour of a participant's hat is determined by a flip of a coin (That is, knowing the colours of the other hats still gives you a 50/50 chance to guess your own one correctly). The rules of the game are as follows: Each participant is allowed to see the hats of the others, but not his own, after they see each other's hat they have to guess the colour of their own hat and write their guess on paper, but they can also write "Forfeit". If none of the participants guesses wrong and at least one did not forfeit (so one must have guessed correctly) they win a prize, otherwise they are sent home empty handed. Before the game, the participants are allowed to discuss a strategy to allow them to win at a high probability. For example, if they decide to all write "Blue" they have a chance of 1/8 to win, However if they choose that one predetermined participant guesses "Blue" and the others forfeit, they have the chance of 1/2 to win. You have to find a better strategy than those two mentioned.
(Hint: The probability of a participant to guess correctly is always 1/2. How can you avoid this obstacle?).

Riddle 4:

The king, who is also a father of three sisters, arranges you to marry one of them, of your choice. The young one always speaks the truth, The older one always lie, and the middle one randomly says "Yes" or "No", whenever addressed to. Obviously you do not want to marry the middle one, but you are willing to marry the other two. You come to the palace and find them all waiting for you, one next to the other. Unfortunately you have never seen them before so you can't tell which is which. You are allowed to ask one of the sisters one Yes/No question and then choose the one you wish to marry. They all look good, cook fine meals, and have a rich daddy, so your only concern is not to marry the middle one. What is the question you should ask?

Riddle 5:

Your friend and you are playing a game. There is a round table and a sack full of coins (all the same) and in each turn one player puts a coin on the table without it overlapping another coin and without moving coins that were already placed. When a player cannot place any more coins on the table he's declared the loser. You have the choice weather you want to play first. What strategy could you have that will get you to always win?

Riddle 6:

Your friend and you are playing a different game. There are 100 heaps of coins, arranged in a straight line, and the total number of coins is odd. At each turn, one player takes one of the heaps at one of the ends of the line and keeps the coins. The game ends when there are no coins left, and one of the players has more coins than the other (since the total number of coins is odd, this will always happend). The person with most of the coins is the winner. You have the choice weather you want to play first. What strategy could you have that will get you to always win?

Riddle 7:

You work at the post office. Your job is to calculate the price for the shipment of packages, by their weight (rounded up to Kilograms). Because of cutbacks in the weighing department, you must weigh the packages yourself. Post office regulations allow you to have one scale with two plates (such as the one you may find on the statue of liberty) and four calibrated weights. Luckily for you, any package weighing more than 40 Kilograms is not allowed for shipment in your station so you can send these to another station without calculating its price. What calibrated weights should you have, that will allow you to calculate the price of a given package every time? (Or send it to another station).

Riddle 8:

You are given thirteen steel balls. You know that one of them has a different weight than the other twelve. You have a coin operated scale with two plates (such as the one you may find on the previous question) and you must find out which of the balls has the different weight, but you have only three coins, so you can use the scales only three times. (Hint: There is a combinatorial solution, which may not be so elegant, but it will always work)

Riddle 9:

100 Men are sent to prison. The prison manager, who loves riddles, gives them an opportunity to get away from prison. There is a room inside the prison with a big clock that is stopped (its hands will not move as time passes). It is not knowns to any prisoner at what hour did the clock stop. Once in a while, one prisoner is called to the room and MUST move the hour hand of the clock by exactly 3 hours (foreward or backwards). The order in which the prisoners are called is pre-defined and known only to the manager, and he guarentees that every man will be called "infinitely many times" (that is, for each prisoner, and for each integer N, there is a point in time for which it is guarenteed that the prisoner will be called at least N times by then). At any point in time, any prisoner can come to the prison manager and declare "Every prisoner has been called to the room", at this point, if every men has been in the room they all get free, otherwise they are shot instantly. The prisoners are allowed deliberations to plan a good strategy for that "game", and after that they are forbidden any communication between them. Show a good strategy that will never get the prisoners killed (that is, a prisoner will never claim that they were all called when it is not the case) and will eventually get them free, no matter in what order they are called (assuming they all will be called infinitely).

Riddle 10:

You are given a circular rope (a ring) and 100 locks. The rope is as long as you want, and as thin as you want, yet it is very strong. Can you put the locks on the rope, in a way that it is impossible to remove any lock from the rope (while the locks are locked), yet, when any (one) lock is unlocked, all of the other locks can be removed without unlocking them? It is forbidden to have interlcoking locks.

Riddle 11:

When two people want to divide a cake among them, they do it the following way: one cuts the cake to two pieces, and one chooses the piece he wants. This way, every person can be sure that if he does the smart choice, he can get at least half of the cake. Now, 3 people are trying to divide a cake, in such way that every person can be sure that if he does the right choices, he will always get at least third of the cake. This solution must not use any tool of measure - players are allowed only to cut and talk (they can say "I choose this part!"). This must be done only in turns (they can't talk or cut at the same time), and must end after a finite (bounded!) number of moves. (Remark: this riddle has many solutions, but many more non-solutions. If you think you've solved it, you have to be able to prove that your solution actually works. I'll be very happy to hear from you if you did solve it since possibly it is a solution I was not aware of).

Riddle 12:

There is a tube of length 10 meters, and 100 ants. The tube is too thin for two ants to be able to squeeze through at the same point. The right end of the tube is open, and at the left end there is a wall. All the ants move in the same constant speed at all times. When an ant collides in another ant or the wall, it changes its direction (by 180 degrees) and walks in the same constant speed. I put the ants inside the tube, in positions and directions of my choice (known to you) and ask you - what is the length that the leftmost ant walks before it reaches the open end of the tube? (the length is not the distance between the ant's starting point and the exit, but how much did it actually walk inside). The answer may depend on the positions and directions of the other ants.

Riddle 13:

Me and my friend have prepared a magic trick. We let you select any 5 cards out of an ordinary deck (which has 52 different kind of cards). I then, am going to tell my friend 4 cards out of the five you gave me and nothing more. To prevent me telling him special signals, I am announcing each card in the standard way, its rank (first) and suit (second), and of course every card has only one name in that way. For example I can say "King of Hearts" and "10 Spades" but not "The king of all the hearts" or "Spades, ten of which". After I announce the cards, he will be able to tell me what is the fifth card, and he will always be correct. I am not allowed to signal him with body language or anything other than telling him the four cards. How can we do that? (Remark: It is possible to do this trick with 124 cards instead of 52)

Riddle 14:

Four grasshoppers are sitting on the grass, forming the shape of a perfect square. A grasshopper can move only in a certain way - he can jump above another grasshopper, landing exactly opposite of where he was before (relative to the grasshopper he jumped above). Can the grasshoppers move to create a larger square?

Riddle 15:

You are given 13 red marbles, 15 blue marbles, and 17 green marbles. Your neighbor is a marble merchant and he offers you the following deal: you can give him two marbles of different colors and recieve a two marbles of the third color (for example, you can give him a blue and a red and recieve two greens). Can you have all marbles in the same color just by these exchanges?
 
 

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