Stage Four

 
Problem No. 3
Not the Dart

 

This is the layout of a dart board:

The red bullseye in the centre scores 50.

The narrow black ring around the bullseye scores 25.

The narrow ring halfway out from the centre doubles the score of that section.

The narrow ring at the outside triples the score of that section.

 

Fred threw 3 darts to score 139.

Where could his darts have landed? Can you find a number of different combinations that will give this score?

 

Can you find 3 different ways of scoring 105?

 

What totals up to 180 cannot be scored using 3 darts?

 

 

All Stage 4 Problems

 

 

Some solutions:

 

From Steven and Neal at Delroy High School

 

Fred's darts could have landed on 3x20 (2 darts)+ 19 (one dart)

Three different ways of scoring 105 are:

 1. 2 bullseyes and a 5

 2. 3x20, 2x20 and a 5

 3. 25, 3x20 and 1x20

 

Three 20 x 3

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A good solution here, well done.

The easiest way I can see of finding all the solutions to this problem is to firstly list all the possible scores:

50, 25, 0 (if you miss the board!) and:

Normal
Double
Triple
1
2
3
2
4
6
3
6
9
4
8
12
5
10
15
6
12
18
7
14
21
8
16
24
9
18
27
10
20
30
11
22
33
12
24
36
13
26
39
14
28
42
15
30
45
16
32
48
17
34
52
18
36
54
19
38
57
20
40
60

Then from here on it would seem to be trial and error is the way to go, testing all the possible combinations.