Const Zero=1E-9;
Var
 a, b, c, d, r,
 cx, cy, cz,
 sx, sy, sz,
 nx, ny, nz,
 vx, vy, vz: Double;

Procedure Taxis(t:Double);
 Var
  mx, my, mz: Double;
 Begin
  If t < 0 Then Exit;
  mx := sx + vx * t;
  my := sy + vy * t;
  mz := sz + vz * t - 5 * sqr(t);
  If Sqr(mx - cx) + Sqr(my - cy) + Sqr(mz - cz) < Sqr(r) Then
   Begin
    WriteLn('HIT');
    Halt;
   End;
 End;

Begin
 Read(cx, cy, cz, nx, ny, nz, r, sx, sy, sz, vx, vy, vz);
 a := -5 * nz;
 b := vx * nx + vy * ny + vz * nz;
 c := (sx - cx) * nx + (sy - cy) * ny + (sz - cz) * nz;
 If Abs(a) < Zero
  Then If Abs(b) < Zero
        then Begin
              If Abs(c) < Zero Then
               Begin
                writeln('HIT');
                Halt;
               End;
             End
        Else Taxis(-c / b)
  Else Begin
        d := Sqr(b) - 4 * a * c;
        If (d >= 0) or (Abs(d) < 1E-16) Then
         Begin
          d := Sqrt(d);
          Taxis((-b - d) / 2 / a);
          Taxis((-b + d) / 2 / a);
         End;
       End;
 WriteLn('MISSED');
End.

Read rule 5:

To hit the dartboard the dart should hit it strictly inside boundary from any side.

This is your mistake. Check the conditions of hit in your code one more time.

Good luck!

Thank you vary much!
I got Accepted.

To Sandro(USU):
Well, well it seems to me that there is a little bit of misunderstanding. First I thought that if the dart trajectory belongs to the plane (and that's exactly the test 56), it can be a hit, if it crosses the circle. Turns out not, in that case it's always MISSED...
I do agree that such way the problem is easy to solve. But it can become much tougher, if you change the statement a little bit - to check if the dart crosses the circle, IF the dart is on the plane (infinite number of points). In that case you will have to solve the polinomial not of the 2-nd, but of the 4-th degree (a much more formidable task)... Such a test would be a nice one. I understand that it may not be compatible with the statement for someone, but it would become then a really good problem even for sophisticated programmers...

Edited by author 29.12.2006 18:30

Edited by author 29.12.2006 18:30

To SPIRiT:

The problem statement is OK for test 56. If you change the statement it will be another problem. It's better to save this problem and make a new one about intersection parabola and circle. You can do it. :)