Mathematical Puzzle

Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.
May 15 16 19
June 17 18
July 14 16
August 14 15 17
Cheryl then tells Albert and Bernard separately the month and the day of her birthday, respectively.
Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know, too.
Bernard: At first, I didn’t know when Cheryl’s birthday is, but I know now.
Albert: Then I also know when Cheryl’s birthday is.
When is Cheryl’s birthday?
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The owner of a banana plantation has a camel. He wants to transport his 3000 bananas to the market, which is located after the desert. The distance between his banana plantation and the market is about 1000 kilometer. So he decided to take his camel to carry the bananas. The camel can carry at the maximum of 1000 bananas at a time, and it eats one banana for every kilometer it travels.
What is the most bananas you can bring over to your destination?
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There is a building of 100 floors
If an egg drops from the Nth floor or above it will break.
If it’s dropped from any floor below, it will not break.
You’re given 2 eggs.
Find NHow many drops you need to make?
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Prove that p^2 – 1 is divisible by 24 if p is a prime number greater than 3?
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Three people check into a hotel.
They pay £30 to the manager and go to their room.
The manager suddenly remembers that the room rate is £25 and gives £5 to the bellboy to return to the people.
On the way to the room the bellboy reasons that £5 would be difficult to share among three people so he pockets £2 and gives £1 to each person.
Now each person paid £10 and got back £1.
So they paid £9 each, totalling £27. The bellboy has £2, totalling £29.
Where is the missing £1?
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People are waiting in line to board a 100seat airplane. Steve is the first person in the line. He gets on the plane but suddenly can’t remember what his seat number is, so he picks a seat at random. After that, each person who gets on the plane sits in their assigned seat if it’s available, otherwise they will choose an open seat at random to sit in.
The flight is full and you are last in line. What is the probability that you get to sit in your assigned seat?
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