Darts

 Introduction The dartboard most commonly found in pubs, clubs and homes is the clock or trebles board. It consists of a circle of 20 segments numbered from 1 to 20 in a seemingly random fashion. The small red circle at the centre is called the bullseye; the thin green ring that surrounds this is the 25 ring. The treble ring is about half way to the edge of the board and the double ring is at the rim of the circle. If a dart lands, for instance, in the segment marked 17 and is within the treble ring, a treble 17 (51) has been scored. A picture of a standard dartboard is shown below.

 Exercises Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

Question 1
With 3 darts, and assuming that every dart scores, what is
 (a)  the highest possible score? (b)  the lowest possible score?

Question 2
With just one dart it is possible to score 50 (with the bullseye) or 51 (with a treble 17).
 What other scores between 50 and 60 are possible with just one dart?  50, 51, Separate your answers with a comma

Question 3
 Find the lowest score it is impossible to obtain with just 1 dart.

Question 4
 Using up to but not more than 3 darts, what is the lowest score it is impossible to get?

Question 5
With 3 darts you can score 180 (60 + 60 + 60) and 160 (60 + 60 + 40). There are 10 other scores between 160 and 180 which you can obtain with 3 darts.
 Find as many of these scores as you can, filling in the boxes to show how they can be obtained. + + + + + + + + + + + + + + + + + + + +

Question 6
In the game ‘501’ two players each start with a score of 501 and, taking it in turns, throw 3 darts at the board. The total score is deducted from 501. The winner is the one who reaches a score of exactly zero, with their final dart landing in the ‘double ring’ or the ‘bullseye’.

 In a game of ‘501’, in how many ways is it possible to get to zero, finishing with a double or bullseye, when your score is 15?   HINT: The order in which the 3 darts go into the board is important!

Question 7
 What is the lowest number of darts thrown with which it is possible for a player to complete a game of 501?

Question 8
The darts board has a specific design in which high numbers are usually next to low numbers. There are 20 sectors on the board. Any 5 adjacent sectors make up one quarter of the board.

 List the 5 numbers that make up the quater of the board whose sum is the greatest

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