HatGame | Topcoder Archive

Problem Statement

You and your friend are playing a game. There are 12 pieces of paper in a hat numbered 1 through 12. Each of you randomly picks 6 pieces of paper from the hat and averages the values on the papers. Whoever has the higher average wins. Given 4 of the numbers you picked from the hat, determine how many combinations of 2 other numbers you can pick and win. Ties do not count as wins. Averages are computed as real numbers and not integers. See the examples for further clarifications.

Create a class HatGame that contains the method numWays, which takes an int[] nums, and returns an int that represents the number of ways to pick 2 other numbers and win.

Definition

Class:: HatGame
Method:: numGroups
Parameters:: int[]
Returns:: int
Method signature:: int numGroups(int[] nums)
(be sure your method is public)

Constraints

nums must contain 4 elements
Each element of nums must be between 1 and 12 inclusive
nums must not contain any duplicate values

Examples

```
{1,2,3,4}
```
```
Returns: 0
```
There are no numbers you can pick that will allow you to beat the other player.
```
{12,11,10,9}
```
```
Returns: 28
```
```
{1,4,8,12}
```
```
Returns: 11
```
```
{2,4,6,8}
```
```
Returns: 5
```
```
{1,12,2,11}
```
```
Returns: 12
```
```
{1,2,4,12}
```
```
Returns: 1
```

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