Solution:

Tea Pot

Solution:

Caesar is a King
Brutus is a Spy
Cassius is a Bureaucrat

Brutus is not the king, since if he is, then Caesar would also be the king.
Cassius is not the king, since his statement would then be a lie.

Therefore Caesar is the king. Hence Cassius is the bureaucrat, and Brutus is the spy.

Solution:

Rose bought lilies, Lily bought jasmines and Jasmine - roses. By the condition, the girl, who bought the roses isn't Rose. She's not Lily either, because Lily answered to that girl. So, the roses were bought by Jasmine, and thus lilies were bought by Rose and jasmines by Lily.

Solution:

(8 - 0) - (5 - 4) - (9 - 5) = 3

Solution:

Up for grabs

Solution:

"A Tennis Ball" Or a "Badminton shuttle"

Solution:

the word is 'incorrectly'

Solution:

Of course, it is impossible. Into the second room should have gone the 2nd guest, because the 13th guest was waiting in room number 1

Solution:

Six.

There are only five colors, so six socks guarantee that two will be the same color.

Solution:

Queue (remove the last four letters – the pronunciation is the same)