25/02/2013 - Cards (*)

This puzzle is rated 1 star (easy).

Description

This is a classic puzzle.  You need to know there are 4 lots of 13 different types of card in a standard 52 card deck.

Puzzle
In two decks of cards, what is the least amount of cards you must take to be guaranteed at least one four-of-a-kind?

Check the solutions page for the correct answer.

27/01/2013 - Pool Balls (**)

This puzzle is rated 2-star (medium).

Description

A cloth bag contains a single red pool ball. 

A second pool ball is chosen at random in such a way that it is equally likely to be a red or a yellow ball. The ball is added to the bag, the bag is shaken, and a ball is drawn at random. 

The withdrawn ball proves to be a red.

Puzzle

What is the probability that the ball remaining in the bag is also a red?

Check the solutions page for the correct answer.