Archive for the 'Puzzles' Category



16
Dec
09

Solutions to WU’s puzzles and riddles : Where’s the Father (medium)

Where is the Father

I am trying to find all the solutions and put them together at a single place, So feel free to add comments and if you have a solution please do post. Cheers … :)

Here is the puzzles link : http://www.wuriddles.com/


Question : The mother is 21 years older than the child. In 6 years from now, the mother will be 5 times as old as the child. Question: Where’s the father?

My Solution : If you calculate the value of the age of the baby, you will get – 3/4 = – 0.75 = 9 months

This is derived from this equation :

27+x = 5 (x+6)      =>  27+x = 5x+30  => 4x = -3  => x = -3/4 = 9 months before the baby was born.

Hence the Father is with the Mother

16
Dec
09

Solutions to WU’s puzzles and riddles : Brown eyes and Red eyes (medium)

BROWN EYES AND RED EYES

I am trying to find all the solutions and put them together at a single place, So feel free to add comments and if you have a solution please do post. Cheers … :)

Here is the puzzles link : http://www.wuriddles.com/

Question:There is an island of monks where everyone has either brown eyes or red eyes. Monks who have red eyes are cursed, and are supposed to commit suicide at midnight. However, no one ever talks about what color eyes they have, because the monks have a vow of silence. Also, there are no reflective surfaces on the whole island. Thus, no one knows their own eye color; they can only see the eye colors of other people, and not say anything about them. Life goes on, with brown-eyed monks and red-eyed monks living happily together in peace, and no one ever committing suicide. Then one day a tourist visits the island monastery, and, not knowing that he’s not supposed to talk about eyes, he states the observation “At least one of you has red eyes.” Having acquired this new information, something dramatic happens among the monks. What happens?Hint: First consider the case where there are only a few monks on the island, some with brown and some with red. Work through the logic and find out what happens over time. Then generalize for the case of M monks on the island, N of which have red eyes.

What happens if we change the tourist’s statement to each of the following?

“There are 10 Brown Eyed Monks”

“There are at lesat two Red Eyed Monks”

“There is an odd number of Red Eyed Monks”

“There is an even number of Red Eyed Monks”

“There is more than one Red Eyed Monk”

My Solution : If there are N people with red eyes among the group, then all the N people will commit suicide on the the N th night.  Lets consider different scenarios.

If there is only one Red Eye monk, after the tourist announcing that there is at least one red eyed monk, this monk will look every one and finds that every one has blue eyes, which implies that he has the red eyes. So he will commit suicide that island on that  night. So if there is only one Red eyed monk, it takes one day to decide.

Now lets consider, there are 2 red eyed monks. The first red eyed guy thinks in this way : I can see a guy with red eye and the remaining with blue eyes. So that red eyed guy must commit suicide today( by the first scenario). The second guy also thinks in the same way. So both will wait until tomorrow and no one commits suicide. Then the next day, both of them think in this way : If he is the only red eyed guy, he must have committed suicide by now, since he did not leave, there must be another red eyed guy, but i can see only one red eyed guy, that implies i am a red eyed guy. so the second night, both of them commit suicide.

Similarly, if there are 3 people, all the 3 people will commit suicide on the 3rd night. and the rest of the problems can be solved in the same way.

If you have any queries regarding the solution, please do post your comments.

16
Dec
09

Solutions to WU’s puzzles and riddles : Faustian Round Table Coin Game (medium)

FAUSTIAN ROUND TABLE COIN GAME

I am trying to find all the solutions and put them together at a single place, So feel free to add comments and if you have a solution please do post. Cheers … :)

Here is the puzzles link : http://www.wuriddles.com/

Question : you die and the devil says he’ll let you go to heaven if you beat him in a game. the devil sits you down at a round table. he gives himself and you a huge pile of quarters. he says “ok, we’ll take turns putting quarters down, no overlapping allowed, and the quarters must rest on the table surface. the first guy who can’t put a quarter down loses.” you guys are about to start playing, and the devil says that he’ll go first. however, at this point you immediately interject, and ask if you can go first instead. you make this interjection because you are very smart, and you know that if you go first, you can guarantee victory. explain how you can guarantee victory.

My Solution : If we put the first coin on the table, then we will definitely win. Try to visualize a carom board with red piece in the center and several white pieces around it. if the white pieces are kept around the red piece, there will be exactly 6 pieces to cover the entire circle around the red piece. so any coin put can be put concentric to these pieces. So essentially there will be a coin at the center, six coins around it,  and some even number of coins concentric to the first circle and another  even number of coins concentric to the first 2 circles and so on ……. So we start the game by putting the center coin, and we take turns with the devil to place coins, and as the number of coins around the center one is always even, we will put the last coin and hence can win the game.

16
Dec
09

Solutions to WU’s puzzles and riddles : Globe Traversal (medium)

Globe Traversal

I am trying to find all the solutions and put them together at a single place, So feel free to add comments and if you have a solution please do post. Cheers … :)

Here is the puzzles link : http://www.wuriddles.com/

Question :how many places are there on the earth that one could walk one mile south, then one mile west, then one mile north and end up in the same spot? to be precise, let’s assume the earth is a solid smooth sphere, so oceans and mountains and other such things do not exist. you can start at any point on the sphere. also, the rotation of the earth has nothing to do with the solution; you can assume you’re walking on a static sphere if that makes the problem less complicated to you. Hint 1: think you’ve figured it out? do you know that there’s more than one? in fact, there are more than two. also note that walking north from the north pole (or south from the south pole) is illogical and therefore does not enter into the problem. all normal assumptions about directions will be used.

Hint 2: christopher columbus.

My Solution: There are infinitely many points in which the above condition is possible if we assume that the earth is a perfect sphere and while travelling the distance, there are no obstructions like mountains etc…. For any point, lets draw the longitude originating  from that point. then it will be like a north pole. So if we move south and then west and again north, we will end up at the same point. For visual explanation look at the globe at the north pole and observe the longitudes and latitudes.

16
Dec
09

Solutions to WU’s puzzles and riddles : GLASS HALF FULL (easy)

Glass Half Full

I am trying to find all the solutions and put them together at a single place, So feel free to add comments and if you have a solution please do post. Cheers … :)
Here is the puzzles link : http://www.wuriddles.com/

Question : You are in an empty room and you have a transparent glass of water. The glass is a right cylinder, and it looks like it’s half full, but you’re not sure. How can you accurately figure out whether the glass is half full, more than half full, or less than half full? You have no rulers or writing utensils.

Hint 1: To help you get started if you’re stuck, here’s a solution that’s not good enough. Holding the cup upright, use the palm of your left hand to cover the cup’s opening. Now make a pinching gesture with the index finger and thumb of your right hand. Put the thumb at the base of the cup, and the index finger adjacent to the water level, thereby gauging the height of the water surface from the base of the cup. Now freeze the distance between those two fingers. Flip the cup upside down with your left hand; no water falls out since you’ve sealed the opening with your left palm. Now put your frozen right hand against the cup, and see if the inverted water level is next to your index finger. If so, the cup is exactly half full. This seems like a good solution, but it’s actually slightly accurate, because the palm of your hand is not a perfectly flat surface. Also, you’ll most likely lose some water when you flip the cup upside down. We want a really accurate method.

Hint 2: Utilize the geometry of the cup. That’s really important.

Hint 3: Don’t drink the water. ^_^

My Solution : Tilt the glass till the water comes upto the brim. If the glass is exactly half filled, then the 2 ends of the water will be the brim and the upper bottom of the tilted glass. If the water is less than half, the water level will be lower than the upper bottom of the tilted glass and vice versa. This is possible because, the glass is a right circular cylinder, which means that the length of the radius is equal to the height of the cylinder. Another explanations is through the volumes. If the glass is half full, then the volume of the water must be ∏ rˆ3/2 . And if the tilted glass has the water level touching the brim and the upper bottom of the glass then their volume will also be V/2 .

16
Dec
09

Solutions to WU’s Puzzles and Riddles : CORK, BOTTLE, COIN ( easy)

CORK, BOTTLE, COIN

Hi guys this is my first solution to the WU’s Puzzles.

I am trying to find all the solutions and put them together at a single place, So feel free to add comments and if you have a solution please do post . Cheers … :)

Here is the puzzles link : http://www.wuriddles.com/

Question : If you were to put a coin into an empty bottle and then insert a cork in the bottle’s opening, how could you remove the coin without taking out the cork or breaking the bottle?

Hint: Actually, people solve this riddle everyday. Let’s say you’re opening a wine bottle, and in the process you break the cork. What’s the only thing left to do?

My Solution : One thing is we can heat the neck of the bottle, so that the opening expands and cork drops inside and the coin can be removed.

But if consider not to damage the bottle, the simple answer is just to push the cork, inside the bottle and take the coin out.




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