Generate a series of random numbers that add up to N in c#

Question

How do I generate 30 random numbers between 1-9, that all add up to 200 (or some arbitrary N), in C#?

I\'m trying to generate a string of digits that can add togethe

Answer 1

My Original Statement:

You can only generate 29 random numbers. The 30th number will be defined by the other 29 and the sum. This is statistically important...

I wanted to add some clarification after thinking about it and pinging the community...

I now believe my original statement to be false. It was too lenient(which lc pointed out). You can't even generate 29 truly random numbers. As you get closer and closer to 30, the final digits aren't random the same way that rnd[1..9] is random. lc tried to mitigate this in order to come up with a solution, but I believe the solution he came up with (and Spencer) answers a very different question. That question is "Of all the sets of 30 digits between 1 and 9 that add up to 200, construct one randomly".

What I believe to be the case is that the question as stated is unsolvable which I believe can be proved with the Pigeonhole Principle (also used by Knuth to show that certain "random" shuffles weren't really random), but I haven't done the math.

Good talk everyone.