Fun Math Problems
Average Speed
You
go hiking on a 6-km mountainous trail. When you climb the mountain, you
go at 2 km per hour, and when you come down, you go at 3 km per hour.
What is your average speed?
A Spider
A spider crawls up
a 20-feet wall. It craws up 6 feet during the day, and drops 4 feet at
night. How many days does it take for the spider to get to the top of
the wall?
Cheryl's Birthday
Albert and Bernard just
become friends with Cheryl, and they want to know when her birthday is.
Cheryl gives them a list of 10 possible dates:
May 15 May 16 May 19
June 17 June 18
July 14 July 16
August 14 August 15 August 17
Cheryl then tells Albert and Bernard separately the month and the day of her birthday respecitively.
Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.
Bernard: At first I don't know when Cheryl's birthday is, but I know now.
Albert: Then I also know when Cheryl;s birthday is.
So when is Cheryl's birthday?
Distributing dollars
Bob has 10 pockets and 44 silver dollars. He wants to put his dollars into his pockets so distributed that each pocket contains a different number of dollars. Can he do so? (Taken from How to Solve it, by G. Polya)
Monty Hall Problem
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? (Taken from Wiki)