Pints of beer

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?




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There are eight rooms in the house in which the murder has been committed: Kitchen, Living Room, Bathroom, Garage, Basement, 3 Bedrooms.

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Can you identify the murderer and the four liars? Also, can you find out who was in which room?

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Joseph:
Peter was in the 2nd bedroom.
So was I.
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Mandy:
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But I think that Joseph was in the living room, OH MY GOD!

Peter:
Mandy was in the kitchen with Christopher.
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David:
I still say Peter was in the 2nd bedroom and Jennifer was in the bathroom.
Joseph was in the 1st bedroom.

Jennifer:
Peter was in the bathroom with Christopher.
And Mandy was in the kitchen.

Christopher:
David was in the kitchen.
And I was in the 2nd bedroom with Peter.

PS: The corpse was found in the Living Room.

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There is a cryptic organization called Cicada 3301 that posts challenging puzzles online, possibly to recruit codebreakers and linguists.