BMAT 2012 · Question 25 · Logic
SaveIn a variation of the game of darts, players throw their darts at a board which has three non- overlapping circles on it. The circular regions have values of 2 points, 4 points and 6 points, as shown in the diagram below:
On each turn a player throws three darts and once all three darts have been thrown their score is added to the player's overall score. If a dart lands in a circle then the player scores the value of that circle, but if the dart lands outside all of the circles then the player's score for the turn so far is halved. If two or more darts land outside the circles then the player scores zero. The first player to score 101 points wins the game. How many different scores in a full turn, apart from 0, are possible?