drilling the hole

HOLE IN A SPHERE

A 6-inch hole is drilled through a sphere. What is the volume of the remaining portion of the sphere?
Clarifications:
[1] the hole is a circular cylinder of empty space whose axis passes through the center of the sphere - just as a drill would make if you aimed the center of the drill at the center of the sphere and made sure you drilled all the way through.
[2] the length of the hole [6 inches] is the height of the cylinder that forms the inside surface once the hole is drilled. picture the inside surface as viewed from inside the hole and measure the length of that surface in the direction of the axis of the drill.
in this sense, you could for example drill a 6-inch hole through the earth. the diameter of the hole would be huge, and you'd just have a tiny remnant of the earth left. but if you could set it on a table [a big table] it would be 6 inches high.
You of course could not drill a 6-inch hole through a sphere whose diameter was less than 6 inches. This fact leads to the logical answer.
The hard way involves calculus. The easy way uses logic.

The awkward execution....but a bit more puzzling

HATS ON A DEATH ROW

You are one of 20 prisoners on death row with the execution date set for tomorrow. Your king is a ruthless man who likes to toy with his people's miseries. He comes to your cell today and tells you:
"I'm gonna give you prisoners a chance to go free tomorrow. You will all stand in a row (queue) before the executioner and we will put a hat on your head, either a red or a black one. Of course you will not be able to see the color of your own hat; you will only be able to see the prisoners in front of you with their hats on; you will not be allowed to look back or communicate together in any way (talking, touching.....).

The prisoner in the back will be able to see the 19 prisoners in front of him. The one in front of him will be able to see 18...

Starting with the last person in the row, the one who can see everybody in front of him, he will be asked a simple question: WHAT IS THE COLOR OF YOUR HAT?

He will be only allowed to answer "BLACK" or "RED". If he says anything else you will ALL be executed immediately.

If he guesses the right color of the hat on his head he is set free, otherwise he is put to death. And we move on to the one in front of him and ask him the same question and so on...

Well, good luck tomorrow, HA HA HA HA HA HA!"

Now since you all can communicate freely during the night, can you find a way to guarantee the freedom of some prisoners tomorrow? How many

Not a big problem..

A Number Problem

(a-x)(b-x)(c-x)(d-x).........(z-x) = ? The Answer is really Very easy But the reason is also required with the answer.That too is an easy part. So Lets Solve this one and see Can U Solve it??

Tricky Ages???

                                          3 Sons and Their Ages

A census worker asked a mother for the ages (years, not months) of her three children. The mother replied that the product of their ages is 36, and the sum of their ages is the same as the address (house number) to the north. After looking at that address, the census worker returned and said to the mother:"I need more information." The mother said: " The oldest is sleeping upstairs." What are the ages of the three children? What is the address (house number) next door to the north?

Lets Test Your Mathematics skills

                                      Find A Number Which.....

Find a number consisting of 9 digits in which each of the digits from 1 to 9 appears only once. This number should satisfy the following requirements: 
a. The number should be divisible by 9. 
b. If the most right digit is removed, the remaining number should be divisible by 8. 
c. If then again the most right digit is removed, the remaining number should be divisible by 7. 
d. etc. until the last remaining number of one digit which should be divisible by 1.

Can U Find the fake one??? i am puzzled

 The Fake Coin

You have twelve coins. You know that one is fake. The only thing that distinguishes the fake coin from the real coins is that its weight is imperceptibly different. You have a perfectly balanced scale. The scale only tells you which side weighs more than the other side.

What is the smallest number of times you must use the scale in order to always find the fake coin?

Use only the twelve coins themselves and no others, no other weights, no cutting coins, no pencil marks on the scale. etc.

These are modern coins, so the fake coin is not necessarily lighter.

Presume the worst case scenario, and don't hope that you will pick the right coin on the first attempt.

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Do you know why????

                                                  Round or Square??

Why is it better to have round manhole covers than square ones?

A lateral Thinking puzzle

                                             How they Identified the murderer?

 Acting on an anonymous phone call, the police raid a house to arrest a suspected murderer. They don't know what he looks like but they know his name is John and that he is inside the house. The police bust in on a carpenter, a lorry driver, a mechanic and a fireman all playing poker. Without hesitation or communication of any kind, they immediately arrest the fireman. How do they know they've got their man?

Can U Solve it??

The Monkeys and the Coconuts

Ten people land on a deserted island. There they find lots of coconuts and a monkey. During their first day they gather coconuts and put them all in a community pile. After working all day they decide to sleep and divide them into ten equal piles the next morning.

That night one castaway wakes up hungry and decides to take his share early. After dividing up the coconuts he finds he is one coconut short of ten equal piles. He also notices the monkey holding one more coconut. So he tries to take the monkey's coconut to have a total evenly divisible by 10. However when he tries to take it the monkey conks him on the head with it and kills him.

Later another castaway wakes up hungry and decides to take his share early. On the way to the coconuts he finds the body of the first castaway, which pleases him because he will now be entitled to 1/9 of the total pile. After dividing them up into nine piles he is again one coconut short and tries to take the monkey's slightly bloodied coconut. The monkey conks the second man on the head and kills him.

One by one each of the remaining castaways goes through the same process, until the 10th person to wake up gets the entire pile for himself. What is the smallest number of possible coconuts in the pile, not counting the monkey's?

Actually the sequel of the last question

The one Gold Coin

The five pirates mentioned previously are joined by a sixth, then plunder a ship with only one gold coin.

After venting some of their frustration by killing all on board the ship, they now need to divvy up the one coin. They are so angry, they now value in priority order:
1. Their lives
2. Getting money
3. Seeing other pirates die.

So if given the choice between two outcomes, in which they get the same amount of money, they'd choose the outcome where they get to see more of the other pirates die.

How can the captain save his skin?

Maximum Coins

                            100 Gold Coins

Five pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all extremely intelligent, treacherous and selfish (especially the captain).

The captain always proposes a distribution of the loot. All pirates vote on the proposal, and if half the crew or more go "Aye", the loot is divided as proposed, as no pirate would be willing to take on the captain without superior force on their side.

If the captain fails to obtain support of at least half his crew (which includes himself), he faces a mutiny, and all pirates will turn against him and make him walk the plank. The pirates start over again with the next senior pirate as captain.

What is the maximum number of coins the captain can keep without risking his life?

Murder in the desert

                           Who is the murderer?

This is a story about three people (A, B and C) crossing a desert. A hated C and decided to kill him - he poisoned the water in his sack (only C had water). B also wanted to kill C (not knowing that the water of C had been already poisoned) and so B made a hole into the sack of C and the water spilt out. A few days later C died of thirst. 
Who was the murderer - A or B?

The Hiking tour!!!!

The Mountain Climbing

On Monday morning at 9:00 am you start at the base of a mountain and begin hiking. Your pace is not regular and you take breaks along the way. Monday evening at 9:00 pm you reach the peak. On Tuesday morning at 9:00 am, after camping overnight, you start at the peak of the mountain and begin your return trip. You follow the exact same path from the previous day, but your pace is faster and you take more breaks. Tuesday evening at 9:00 pm you reach the base. Can you determine if there is a point you were at somewhere on the path at the same time of day Monday and Tuesday. (You are not asked to name the point, just whether or not such a point must exist.)

What Will You Do???

                                      Crates Of Fruit

You are on an island and there are three crates of fruit that have washed up in front of you. One crate contains only apples. One crate contains only oranges. The other crate contains both apples and oranges. 

Each crate is labeled. One reads "apples", one reads "oranges", and one reads "apples and oranges". You know that NONE of the crates have been labeled correctly - they are all wrong.

If you can only take out and look at just one of the pieces of fruit from just one of the crates, how can you label ALL of the crates correctly?

The Three Gods

                 The Three Gods

 Three gods A , B , and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A , B , and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer in their own language, in which the words for yes and no are "da" and "ja", in some order. You do not know which word means which.

The Hardest Logic puzzle

                            The One with Blue Eyes!!

A group of people with assorted eye colors live on an island. They are all perfect logicians -- if a conclusion can be logically deduced, they will do it instantly. No one knows the color of their eyes. Every night at midnight, a ferry stops at the island. Any islanders who have figured out the color of their own eyes then leave the island, and the rest stay. Everyone can see everyone else at all times and keeps a count of the number of people they see with each eye color (excluding themselves), but they cannot otherwise communicate. Everyone on the island knows all the rules in this paragraph.

On this island there are 100 blue-eyed people, 100 brown-eyed people, and the Guru (she happens to have green eyes). So any given blue-eyed person can see 100 people with brown eyes and 99 people with blue eyes (and one with green), but that does not tell him his own eye color; as far as he knows the totals could be 101 brown and 99 blue. Or 100 brown, 99 blue, and he could have red eyes.

The Guru is allowed to speak once (let's say at noon), on one day in all their endless years on the island. Standing before the islanders, she says the following:

"I can see someone who has blue eyes."

Who leaves the island, and on what night?


There are no mirrors or reflecting surfaces, nothing dumb. It is not a trick question, and the answer is logical. It doesn't depend on tricky wording or anyone lying or guessing, and it doesn't involve people doing something silly like creating a sign language or doing genetics. The Guru is not making eye contact with anyone in particular; she's simply saying "I count at least one blue-eyed person on this island who isn't me."

And lastly, the answer is not "no one leaves."

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The Poisoned wine

Problem 7: You are 'The Emperor'

1. The Emperor
You are the ruler of a medieval empire and you are about to have a celebration tomorrow. The celebration is the most important party you have ever hosted. You've got 1000 bottles of wine you were planning to open for the celebration, but you find out that one of them is poisoned.
The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after consuming even the minutest amount of poison.
You have over a thousand slaves at your disposal and just under 24 hours to determine which single bottle is poisoned.
You have a handful of prisoners about to be executed, and it would mar your celebration to have anyone else killed.
What is the smallest number of prisoners you must have to drink from the bottles to be absolutely sure to find the poisoned bottle within 24 hours?
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IMPORTANT

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What will you ask?

Problem 6: The Two Doors

You are trapped in a room with two doors. One leads to certain death and the other leads to freedom. You don't know which is which.
There are two robots guarding the doors. They will let you choose one door but upon doing so you must go through it.
You can, however, ask only one robot one question. The problem is one robot always tells the truth ,the other always lies and you don't know which is which.
What is the question you ask?
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Can U Solve it!!!!!

Problem 5: Here is the Question

The stopping distance of a car is the number of feet that the car travels after the driver starts applying the brakes. The stopping distance of a certain car is directly proportional to the square of the speed of the car, in miles per hour, at the time the brakes are first applied. If the car’s stopping distance for an initial speed of miles per hour is feet, what is its stopping distance for an initial speed of miles per hour?
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Dealing With Geometry

Problem 4: Hardest but the Easiest One

Using only elementary geometry, determine angle x. Provide a step-by-step proof.
You may use only elementary geometry, such as the fact that the angles of a triangle add up to 180 degrees and the basic congruent triangle rules (side-angle-side, etc.). You may not use trigonomery, such as sines and cosines, the law of sines, the law of cosines, etc. There is a review of elementary geometry below.
This is the hardest problem I have ever seen that is, in a sense, easy. It really can be done using only elementary geometry.
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