September 3, 2008 at 16:31Task number 109
- Transfer
I love puzzles with pictures:
In a dart game, a player throws 3 arrows at a target, divided into twenty sections of the same size, numbered from one to twenty.
The points of each dart are determined by the number of the section in which it landed. If the dart landed outside the outer red-green circle, then it scored zero. The black and beige areas inside the circle give a single amount of points. The red-green outer and inner circles give a doubling and tripling respectively.
In the center of the target are two circles called the bulls-eye. The outer of them gives 25, the inner doubling of 25, i.e. 50.
There are many variations of the game, but the most popular one is when players start with a score of 301 or 501 and the first player who reduces their points to 0 wins. However, they usually play according to the “exit by doubling” system, which means that the player must hit the sector with doubling with the last dart (including the double bulls-eye in the center of the target); any other hit that reduces points to one or less means “bust”.
The number of points at which a player can finish with a series of three throws is called “checkout”, with a maximum checkout of 170: T20 T20 D25 (two triple 20s and double bulls-eye).
There are exactly eleven ways to win with 6 points 6:
Note that D1 D2 is considered different from D2 D1, since they end in different doublings. However, the combination S1 T1 D1 is identical to T1 S1 D1.
Additionally, we prefer not to include misses in the combination; for example, D3 is identical to 0 D3 and 0 0 D3.
In total, there are 42,336 different ways to finish.
And how many ways are there to finish with less than 100 points?
I consider the decisions to publish and discuss incorrect ... There is a special forum on projecteuler.net
PS: It was necessary to make topics closed, now everything is covered.
In a dart game, a player throws 3 arrows at a target, divided into twenty sections of the same size, numbered from one to twenty.
The points of each dart are determined by the number of the section in which it landed. If the dart landed outside the outer red-green circle, then it scored zero. The black and beige areas inside the circle give a single amount of points. The red-green outer and inner circles give a doubling and tripling respectively.
In the center of the target are two circles called the bulls-eye. The outer of them gives 25, the inner doubling of 25, i.e. 50.
There are many variations of the game, but the most popular one is when players start with a score of 301 or 501 and the first player who reduces their points to 0 wins. However, they usually play according to the “exit by doubling” system, which means that the player must hit the sector with doubling with the last dart (including the double bulls-eye in the center of the target); any other hit that reduces points to one or less means “bust”.
The number of points at which a player can finish with a series of three throws is called “checkout”, with a maximum checkout of 170: T20 T20 D25 (two triple 20s and double bulls-eye).
There are exactly eleven ways to win with 6 points 6:
 D3 | | |
| D1 | D2 | |
| S2 | D2 | |
| D2 | D1 | |
| S4 | D1 | |
| S1 | S1 | D2 |
| S1 | T1 | D1 |
| S1 | S3 | D1 |
| D1 | D1 | D1 |
| D1 | S2 | D1 |
| S2 | S2 | D1 |
Note that D1 D2 is considered different from D2 D1, since they end in different doublings. However, the combination S1 T1 D1 is identical to T1 S1 D1.
Additionally, we prefer not to include misses in the combination; for example, D3 is identical to 0 D3 and 0 0 D3.
In total, there are 42,336 different ways to finish.
And how many ways are there to finish with less than 100 points?
I consider the decisions to publish and discuss incorrect ... There is a special forum on projecteuler.net
PS: It was necessary to make topics closed, now everything is covered.