As an intellectual exercise only, I am attempting to solve the following:
by throwing 3 darts at a standard dartboard, it is possible to score a maximum of 180 (3 x treble 20), and a minimum of zero (all darts miss the scoring area).
1. Which total scores within this range are not possible to achieve? (eg 179)
2. For each of the possible scores, how many ways are there to achieve that score? (eg a total of 5 could be
0, 0, 5, or
0, 3, 2, or
0, treble 1, double 1, or
0, 1, double 2
etc etc)
Remember that we are looking at combinations, not permutations, since the order of the 3 darts is irrelevant.
I am working on an Excel solution to this at present and would be interested to see if anyone else has a solution to compare with what I hope will be my solution.
Regards
Best Answer
Here is the result. 9 scores are not possible. 163, 166, 169, 172, 173, 175, 176, 178 and 179. Score with most combinations is 60 (619 ways to score 60 points).
Anyone agree/disagree with this?