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Which Clock is Better ?

Which clock works better?
The one that loses a minute a day or the one that doesn't work at all?

Sum and Product Puzzle

X and Y are two different integers, greater than 1, with sum less than or equal to 100. S and P are two mathematicians; S knows the sum X+Y, P knows the product X*Y, and both are perfect logicians. Both S and P know the information in these two sentences. The following conversation occurs:

S says "P does not know X and Y."
P says "Now I know X and Y."
S says "Now I also know X and Y!"

What are X and Y?

Singapore Birthday Problem : When is Cheryl's Birthday ?

Albert and Bernard just met Cheryl. “When’s your birthday?” Albert asked Cheryl.

Cheryl thought a second and said,
“I’m not going to tell you, but I’ll give you some clues.”
She wrote down a list of 10 dates:

May 15, May 16, May 19
June 17, June 18
July 14, July 16
August 14, August 15, August 17

“My birthday is one of these,” she said.
Then Cheryl whispered in Albert’s ear the month and only the month of her birthday.

To Bernard, she whispered the day, and only the day of her birthday.

“Can you figure it out now?” she asked Albert.

Albert: I don’t know when your birthday is, but I know Bernard doesn’t know, either.
Bernard: I didn’t know originally, but now I do.
Albert: Well, now I know, too!

When is Cheryl’s birthday?

ANSWER!

Lets first analyze all the given birth dates. The dates can be easily viewed as



Now will analyze the conversation in detail

Line 1) Albert Says: I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know too.
All Albert knows is the month, and every month Cheryl mentioned has more than one possible date, so of course he doesn’t know when her birthday is.

The only way that Bernard could know the date with a single number, however, would be if Cheryl had told him 18 or 19, since of the ten date options only these numbers appear once, as May 19 and June 18.

For Albert to know that Bernard does not know, Albert must therefore have been told July or August (not June or May), since this rules out Bernard being told 18 or 19.

Thus, only possible months for Albert are : July and August
And, only possible days for Bernard are : 14, 15, 16 and 17

Thus, the solution space is now reduced to :
Line 2) Bernard: At first I don’t know when Cheryl’s birthday is, but now I know.

Bernard has deduced that Albert has either August or July. If he knows the full date, he must have been told 15, 16 or 17, since if he had been told 14 he would be none the wiser about whether the month was August or July. Each of 15, 16 and 17 only refers to one specific month, but 14 could be either month.

Thus, the solution space is now reduced to :

Line 3) Albert: Then I also know when Cheryl’s birthday is.

When Albert says that he also knows the answer, he doesn't have the Bernard's data still ! He doesn't know that the day with Bernard is 15, 16 or 17. Then, how did he came to conclusion that he also knows the answer. That means he has July as month as there is only one day associated with July. So, he is sure that now I also know the answer.

The answer, therefore is July 16.

5, 15, 1115, 3115, 132115, 1113122115, 311311222115, ?

What is the next number in this sequence:

5, 15, 1115, 3115, 132115, 1113122115, 311311222115, ?

True and False Statements

Which of the following statements are true and which are false?
1. Only one of the statements is false.
2. Exactly two of the statements are false.
3. Only three of the statements are false.
4. Exactly four of the statements are false.
5. All five of these statements are false.

Birbal Solves Farmer’s Well Dispute

A farmer and his neighbor once went to Emperor Akbar’s court with a complaint. “Your Majesty, I bought a well from him,” said the farmer pointing to his neighbor, “and now he wants me to pay for the water.” “That’s right, your Majesty,” said the neighbor. “I sold him the well but not the water!” The Emperor asked Birbal to settle the dispute.
How did Birbal solve the dispute in favor of the farmer?

The Greek Philosophers

One day three Greek philosophers settled under the shade of an olive tree, opened a bottle of Retsina, and began a lengthy discussion of the Fundamental Ontological Question: Why does anything exist?

After a while, they began to ramble. Then, one by one, they fell asleep.
While the men slept, three owls, one above each philosopher, completed their digestive process, dropped a present on each philosopher's forehead, the flew off with a noisy "hoot." Perhaps the hoot awakened the philosophers.
As soon as they looked at each other, all three began, simultaneously, to laugh.

Then, one of them abruptly stopped laughing. Why?

How many 0’s between 1 to 200 ?

How many 0’s are present in numbers from 1 to 200 ?
(including both numbers)

4 Tablets Puzzle

If I give you 4 tablets which consist of 2 for fever and 2 for cold.
All 4 being of the same size, shape, taste, weight and color and have no cover. You have to take 1 cold and 1 fever tablet right now.
How will you choose correctly?

Poisoned Wine Puzzle

You have 240 barrels of wine, one of which has been poisoned. After drinking the poisoned wine, one dies within 24 hours. You have 5 slaves whom you are willing to sacrifice in order to determine which barrel contains the poisoned wine.
How do you achieve this in 48 hours?

Month Puzzle

If January   = 101025
February     = 6525
March         = 13188
April           = 1912
May            = 13125
June           = 10215
July            = ?

Wrotten Apple !

An apple is in the shape of a ball of radius 31 mm.
A worm gets into the apple and digs a tunnel of total length 61 mm,
and then leaves the apple. (The tunnel need not be a straight line.)
Prove that one can cut the apple with a straight slice through the center so that one of the two halves is not rotten.

Which Letter is Missing ?

Which letter is missing from this sequence:

A , A , A , A , _ , A , A , A , A , A , A ,U

Note: the answer is not A or U.

Pick a Good Candy !

How do you place 50 good candies and 50 rotten candies in two boxes such that if you choose a box at random and take out a candy at random, it better be good!
That means probability of choosing a good candy should be highest. There is no restriction in putting the candies in 2 boxes. Any number of candies can be put in any box.

World with All Girls !!

In a world where everyone wants a girl child, each family continues having babies till they have a girl.
What do you think will the boy to girl ratio be eventually?
(Assuming probability of having a boy or a girl is the same)

Playing with Invisible Dice

You have 2 dice. One regular die and a an invisible die. Numbers 1 to 6 are written on the regular die.But you don't know what's written on the invisible dice.
After tossing both, I speak the sum of outcome of both die. It so happens that the outcome is always an integer between 1 to 12, with equal probability (1/12 each).
Can you guess what are the numbers printed on special invisible dice?

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