generate random number with a specific sum

Question

How do I generate 8 random numbers from 1 to 100 The sum of 8 numbers is 200 Not Without repeating the same numbers in each group Showing all possible outcomes.

Answer 1

It depends on what random means here. You can, for instance, put a problem like this:

There is a stick of length 200 We should put 8 - 1 = 7 random marks on it to cut stick into 8 pieces and return the lengths of these pieces.

Let's draw a pictute:

[----------------------------------------------------------]
^     ^     ^      ^       ^       ^       ^       ^       ^ 
0    33    83     135     138     157     177     186     200 <- points

  33    50     52      3      19      20       9       14     <- lengths

Code:

Random random = new Random();

...

int length = 200;
int count = 8;
int prior = 0;

int[] values = Enumerable
  .Range(0, count - 1)
  .Select(_ => random.Next(0, length + 1))
  .OrderBy(item => item)
  .Append(length)
  .Select(item => {
     int savedPrior = prior;

     prior = item;

     return item - savedPrior; })
  .ToArray();

If you want all values being distinct you can try repeating the procedure when they are not:

int[] values;
int length = 200;
int count = 8;

do {
  int prior = 0;

  values = Enumerable
    .Range(0, count - 1)
    .Select(_ => random.Next(0, length + 1))
    .OrderBy(item => item)
    .Append(length)
    .Select(item => {
       int savedPrior = prior;

        prior = item;

        return item - savedPrior; })
    .Distinct()
    .ToArray();
}
while (values.Length != count);