# Numbers Game

One of the longest-running quiz shows on UK TV is called Countdown, and has a “numbers round”. There are some cards laid face down in front of the host - the top row contains ‘large’ numbers (from the set 25, 50, 75, 100), and the rest are ‘small’ (1 to 10). Six cards are picked and displayed: the choice is made by one of the contestants, who typically will ask for one large number and five small ones.

Next, a machine called “Cecil” picks a target number between 100 and 999 at random. The contestants then have 30 seconds to find a way of combining the source numbers using the normal arithmetic operators (+, -, *, /) to make the target number, or to get as close as possible.

Each source number can be used 0 or 1 times.

### Easy Example

```
source 50 9 4 1 10 2
target 402
( 50 * (9 - 1) ) + 2 = 402
-- OR --
( ( ( 50 * 10 ) / 4 ) + 9 ) * ( 2 + 1 ) = 402
```

### Medium Example

```
source 100 5 5 2 6 8
target 522
100 * 5 = 500
5 + 6 = 11
11 * 2 = 22
500 + 22 = 522
```

Resulting in `(5*100)+((5+6)*2) = 522`

Another solution is `(100+6)*5-8 = 522`

### Hard Example

```
source 75 5 4 4 9 7
target 933
9 * 7 = 63
63 * 4 = 252
252 * 4 = 1008
1008 - 75 = 933
```

Resulting in `((9 * 7 * 4) * 4) - 75 = 933`

Another solution is `( ( (9 * 7) * ( (5 * 4) - 4 ) ) - 75 = 933`

Normal arithmetic rules apply, and in particular you are not allowed to use integer rounding. That is, 7 divided by 3 is 2 1/3, not 2.

The program will accept one target number and a list of source numbers, and generate a solution which calculates the target or a number as close to the target as possible. Solve for the 3 examples above. You can consult http://www.crosswordtools.com/numbers-game/ for more games and solutions if you need more for testing.

# Execution

**NOTE: lines starting with **`$`

signify a command prompt line, and lines starting with `>`

signify output from the executed program.

Assuming your main python file is named `numbers_game.py`

, then to execute we would call:

```
$ python numbers_game.py target num1 num2 num3 ... numN
> (mathematical formula)
```

for example:

```
$ # medium example above
$ python numbers_game.py 522 100 5 5 2 6 8
> (100 + 6) * 5 - 8 = 522
```

Whitespace in output is optional.

# Judging

The results will be judged primarily on correctness, then succinctness of solution. Solutions that take longer than a second to execute will be penalized relative to other correct solutions.

# Submission

Write a python program to solve the problem.

Email solution to `contest201502@okcpython.org`

by **March 6th at 12:00:00AM** with **PUG: numbers game** for the subject.

There will be a prizes lottery for the participating contestants.

Solution *must* be runnable on Ubuntu 14.04, with any special requirements documented.