/* stickr.tc - rb - 2/1,4/2010

/* lrb - 2/4/2010 - fixed bug I introduced by replacing j/n with 0 in last line.
/* it's possible to get all triangles, especially when you have low stick counts.

/* good test script: .[int q;for (q=1;q<=5;++q) [main]]

/* see http://yofx.blogspot.com/2009/03/probability-problem.html

dpf int n,d,p
[
  /* Display proper fraction n/d as decimal number with p digit precision
  int w
  w=10*n/d
  if (p)
  [
    MC w,14
    dpf 10*n%d,d,p-1 /* recursive call
  ]
]

stick
[
  /* Function used to determine whether three pieces of broken stick can form a triangle.
  int b1, b2, bx, l, c, r, t
  b2 = b1 = random 1, 180
  while ( b1 == b2 )  /* Make sure b1 and b2 are different points on the stick
    b2 = random 1, 180
  if ( b1 > b2 )  /* Make sure b2 is the larger number
  [
    bx = b2
    b2 = b1
    b1 = bx
  ]
  r = 181 - b2  /* Right piece
  l = b1  /* Left piece
  c = 181 - l - r  /* Center piece
  if (r < (l + c))
    if (l < (c + r))
      if (c < (l + r))
        t = 1  /* The three pieces can form a triangle
  return t
]

main
[
  /* Determine probability of forming triangle from three pieces of stick broken in two random places
  pl "";ps "stickr.tc - rb - 2/4/2010";pl "";pl ""
  int i, j, n
  ps "Enter a seed number. ==> ";last = gn
  pl ""
  if ( last%2 == 0 )
    ++last  /* make number odd
  seed = last
  ps "Enter number of sticks to break (1 to 3000). ==> ";n = gn
  pl ""
  if (n > 3000)
    n = 0
  while (n < 1)
  [
    ps "Invalid entry. Enter number between 1 and 3000. ==> ";n = gn
    pl ""
    if (n > 3000)
      n = 0
  ]
  for ( i = 1; i <= n; ++i )
    j = j + stick
  ps "Total sticks broken: ";pn n;pl ""
  ps "Total triangles formed: ";pn j;pl ""
  pl "Probability of triangle =";pn j/n;ps ".";dpf(j%n,n,4)
  pl ""
]