We were talking over a cup of coffee the other day about darts, and we discussed the popular darts game Around the Board or Around the Clock. We could remember playing this in two related ways.

In the simplest way of playing each player has to hit One followed by Two, and so on, hitting all the numbers from One to Twenty in order. After hitting Twenty the next target is the Outer Bull, followed by the Inner Bull to finish. The first person to hit all the targets in order wins the game.

In the way of playing above it doesn't matter which bit of the numbered segment you hit - Single, Double and Treble One all move you on to Two. A slightly more complicated way of playing gives benefit to hitting Doubles and Trebles. For example, hitting Treble One (that is a score of three) makes the next target Four (that is one more than the three scored). In this way a good player can advance more quickly.

Clearly, in the first method of playing 22 darts is the fewest in which a player can complete the game - 20 numbers plus the two bullseyes.

In the second method of playing what is the fewest darts needed to complete the game?

We believe that it can be done in five darts, but not fewer, as follows:

1. Double 1 (scores 2, next target 3)
2. Treble 3 (scores 9, next target 10)
3. Double 10 (scores 20, next target Outer Bull)
4. Outer Bull
5. Inner Bull