TopCoder Statistics - Problem Statement

You are playing a game of darts. The target in this particular game looks as follows:

There are F regular sectors. These are worth 1, 2, ..., F points.
There are F "double points" sectors. These are worth 2, 4, ..., 2*F points.
There are F "triple points" sectors. These are worth 3, 6, ..., 3*F points.
There is the bullseye in the middle of the target. The bullseye consists of two sectors: the outer bullseye (worth 25 points) and the inner bullseye (worth 50 points).

You have three darts. What is the largest total number of points you can get if you hit three different sectors?

20

Returns: 171

A regular dartboard has numbers 1 through 20. If we want to produce the highest score we can by hitting three distinct sectors, we should hit the triple-20, triple-19, and triple-18 for a total of 3*20 + 3*19 + 3*18 = 171 points.
1

Returns: 78

This tiny target has only five sectors. These are worth 1, 2, 3, 25, and 50 points. Clearly the optimal solution is to score 3 + 25 + 50 = 78 points.
9

Returns: 102

Now the optimal play is to hit the inner bullseye (50), the outer bullseye (25), and the triple-9 (27 points).
2

Returns: 81
3

Returns: 84
4

Returns: 87
10

Returns: 107
11

Returns: 113
12

Returns: 119
13

Returns: 125
14

Returns: 131
15

Returns: 137
16

Returns: 143
17

Returns: 149
18

Returns: 155
19

Returns: 162
47

Returns: 414
74

Returns: 657
97

Returns: 864
100

Returns: 891
8

Returns: 99
98

Returns: 873
24

Returns: 207

Statistics