n random numbers within parameters

Let's say I have a number, such as 100, and I want to have 5 different random numbers generated, but they all must add up to 100, how would I do that? (preferably in PHP. For math wizards/statisticians, I don't n开发者_如何学JAVAeed truly random numbers, but something that looks random).

So this function, would produce something like this:

5, 51, 9, 18, 19 = 100 34, 52, 3, 7, 4 =100

And so forth.

Ideally, something that takes 5, 100 and produces the rest:

generateRandom(100,5)

---

a = RandomInteger[{1, 96}]
b = RandomInteger[{1, 97 - a}]
c = RandomInteger[{1, 98 - a - b}]
d = RandomInteger[{1, 99 - a - b - c}]
e = 100 - a - b - c - d

Samples:

{34,25,26,3,12,Sum =,100}

{90,5,1,1,3,Sum =,100}

{29,16,21,9,25,Sum =,100}

{4,13,71,10,2,Sum =,100}

The numbers are no equally distributed, of course.

Edit

Here is a more homogeneous distribution:

a = RandomInteger[{1, 20}];
b = RandomInteger[{1, 40 - a}];
c = RandomInteger[{1, 60 - a - b}];
d = RandomInteger[{1, 80 - a - b - c}];
e = 100 - a - b - c - d;

Output:

{5,33,2,8,52,Sum =,100}
{14,9,50,5,22,Sum =,100}
{3,23,12,34,28,Sum =,100}
{1,16,4,5,74,Sum =,100}
{6,28,6,9,51,Sum =,100}
{11,25,7,1,56,Sum =,100}
{4,34,12,18,32,Sum =,100}
{6,13,25,26,30,Sum =,100}
{8,27,14,5,46,Sum =,100}
{17,13,23,25,22,Sum =,100}

Here are the frequencies for the numbers:

Edit

Perhaps a better one:

a = Max[#, 1] & /@ Evaluate[RandomInteger[{1, 20}, 5] - 1];
b = 100 - Total@a;
c = Mod[b, 5];
d = (b - c)/ 5;
a = a + d + {c, 0, 0, 0, 0};

Distribution:

Edit

In Mathematica you can easily generate all 5-Tuples that add up 100 as:

IntegerPartitions[100, {5}]

There are 38225 different beasts, without counting permutations

Length@IntegerPartitions[100, {5}]
(* -> 38225 *)

The frequency for each number in those quintuplets is:

Histogram@Flatten@IntegerPartitions[100, {5}]

The curve is very similar if one take permutations into account:

t = Tally@Flatten@(Permutations[#] & /@ IntegerPartitions[100, {5}]); 
ListLinePlot@SortBy[t, #[[1]] &][[All, 2]]

---

Along the lines of belisarius:

  // Generates an array (of $elements elements) full of random numbers whose
  // total is equal to the $total_sum
  function generate_random_array($elements = 5, $total_sum = 100)
  {
    // build result array
    $result = Array();

    // iterate over all elements (except for the last, last will be the delta)
    for ($_ = 0; $_ < ($elements - 1); $_++)
    {
      // typical low value (non-zero)
      $low_value = 1;

      // high value, skewed to have high results first
      //$high_value = ($total_sum - ($elements - $_) - array_sum($result));
      // high value, non-skewed
      $step = (int)floor($total_sum / $elements); // give "not-to-exceed" ranges
      $high_value = (($_ + 1) * $step) - array_sum($result);

      // produce the result and add it
      $result[] = rand($low_value,$high_value);
      //$result[] = rand(1,65535) % $high_value + 1; // alternate to make rand a little smoother
    }

    // add the final result as the remainder
    $result[] = $total_sum - array_sum($result);

    // now return it
    return $result;
  }