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12 men on an island riddle

There is an island with 12 islanders. All of the islanders individually weigh exactly the same amount, except for one, who either weighs more or less than the other 11.
You must use a see-saw to figure out whose weight is different, and you may only use the see-saw 3 times. There are no scales or other weighing device on the island.

How can you find out which islander is the one that has a different weight?

100 employees in a conference room

There are 100 employees in a conference room in New York City. You note that 99% of them are managers. How many managers would need to leave the conference in order to reduce the percentage of managers in the hall to 98%?

A Probability Problem With Pearls

"I'm a very rich man, so I've decided to give you some of my fortune. Do you see this bag? I have 5001 pearls inside it.
2501 of them are white, and 2500 of them are black. No, I am not racist. I'll let you take out any number of pearls from the bag without looking.
If you take out the same number of black and white pearls, I will reward you with a number of gold bars equivalent to the number of pearls you took."

How many pearls should you take out to give yourself a good number of gold bars while still retaining a good chance of actually getting them?

Probability Heaven Puzzle

A person dies, and he arrives at the gate to heaven. There are three doors in the heaven. one of them leads to heaven. another one leads to a 1-day stay at hell, and then back to the gate, and the other leads to a 2-day stay at hell, and then back to the gate. every time the person is back at the gate, the three doors are reshuffled. How long will it take the person to reach heaven?

Birthday Puzzle

The day before yesterday I was 25 and the next year I will be 28. This is true only one day in a year. What day is my birthday?

Two Paper Cubes Puzzle

A man has two paper cubes on his desk. Every day he arranges both cubes so that the front faces show the current day of the month. What numbers are required on the faces of the cubes to allow this for all possible days in the calendar?

Misfortune Clock

You have the misfortune to own an unreliable clock. This one loses exactly 20 minutes every hour. It is now showing 4:00am and you know that is was correct at midnight, when you set it. The clock stopped 4 hours ago, what is the correct time now?

Probability Puzzle: Tossing of Coins

A man tosses three coins in the air. When they land, he finds that two of the coins have heads up and one has tails up. What is the probability that when the coins are tossed again, they will land again with two heads up and one tails up.

Please note that the coins are unbiased.

Number Comparisons

You have 32 numbers. What is the least number of comparison needed to find the 2nd smallest out of them?

8 Queens on a Chessboard Puzzle

In chess, queens can move horizontally, vertically, or diagonally, as far as they like, as shown in the picture. We say that a queen can "attack" another piece if it can move into the other piece on the next move. How can you place 8 queens on a chessboard such that none of the queens can attack each other?

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?


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.

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