Challenge

Here is the task, inspired by the well-known British TV game show Countdown. The challenge should be pretty clear even without any knowledge of the game, but feel free to ask for clarifications.

And if you fancy seeing a clip of this game in action, check out this YouTube clip. It features the wonderful late Richard Whitely in 1997.

You are given 6 numbers, chosen at random from the set {1, 2, 3, 4, 5, 6, 8, 9, 10, 25, 50, 75, 100}, and a random target number between 100 and 999. The aim is to make use the six given numbers and the four common arithmetic operations (addition, subtraction, multiplication, division; all over the rational numbers) to generate the target - or as close as possible either side. Each number may only be used once at most, while each arithmetic operator may be used any number of times (including zero.) Note that it does not matter how many numbers are used.

Write a function that takes the target number and set of 6 numbers (can be represented as list/collection/array/sequence) and returns the solution in any standard numerical notation (e.g. infix, prefix, postfix). The function must always return the closest-possible result to the target, and must run in at most 1 minute on a standard PC. Note that in the case where more than one solution exists, any single solution is sufficient.

Examples:

• {50, 100, 4, 2, 2, 4}, target 203
  e.g. 100 * 2 + 2 + (4 / 4)
  e.g. (100 + 50) * 4 * 2 / (4 + 2)

• {25, 4, 9, 2, 3, 10}, target 465
  e.g. (25 + 10 - 4) * (9 * 2 - 3)

• {9, 8, 10, 5, 9, 7), target 241
  e.g. ((10 + 9) * 9 * 7) + 8) / 5

Rules

Other than mentioned in the problem statement, there are no further restrictions. You may write the function in any standard language (standard I/O is not necessary). The aim as always is to solve the task with the smallest number of characters of code.

Saying that, I may not simply accept the answer with the shortest code. I'll also be looking at elegance of the code and time complexity of the algorithm!

My Solution

I'm attempting an F# solution when I find the free time - will post it here when I have something!

Format

Please post all answers in the following format for the purpose of easy comparison:

Language

Number of characters: ???

Fully obfuscated function:

(code here)

Clear (ideally commented) function:

(code here)

Any notes on the algorithm/clever shortcuts it takes.