A woman is sitting in her hotel room and hears a knock at the door. She opens the door to see a man whom she’s never met before. He says, “I’m sorry, I have made a mistake, I thought this was my room.†He then goes down the corridor and into the elevator. The woman goes back into her room and calls security. What made the woman so suspicious of the man?
In a basket of apples,
when counted in twos, there was one extra
when counted in threes, there were two extra when counted in fours, there were three extra
when counted in fives, there were four extra
when counted in sixes, there was five extra.
However, if the apples were counted in sevens, no extra apple was left. Can you calculate the minimum number of apples that were present in the basket?
How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?
