A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls?
You stand in front of two doors. A guard stands next to each door. You know the following things: one path leads to paradise, the other leads to death. You cannot distinguish between the two doors. You also know that one of the two guards always tells the truth and the other always lies. You have permission to ask one guard one question to discover which door leads to paradise. What one question would you ask to guarantee you enter the door to paradise?
John is 45 years older than his son Jacob. If you find similarities between their ages, both of their ages contain prime numbers as the digits. Also, John's age is the reverse of Jacob's age.
A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
(a) If 10 matches are played in total, how many players participated?
(b) If 20 players took part in the tournament, how many matches were played?