Sink the conic!

Directions


Sink the conic is very similar to the game Battleships:

  1. the battlefield is a square with co-ordinates |x| <= 50 |y| <= 50
  2. each player must place two conics (his ships) in his own field, according to his skill level
  3. the aim is to locate the rival ships and sink them
  4. in order to discover where the rival ships are, the player must shoot straight lines transmitting their equations; the opponent will reply telling him the co-ordinates of the intersections between the line and his own fleet
  5. when a player thinks he knows the location af a rival ship, he shoots, transmitting its equation; if it is the right one, the ship is sunk
  6. the winner is the player who will sink all the enemy fleet first; if both players sink the rival fleet with an equal number of shots, the winner will be the speedier player


 




Rules














 

Game management

  1. The Game Master assigns a name to each match (Game Id) and to each player (Player Id). The Player Id is the password that allows the player's identification and avoids alien intrusion in the game
  2. At the beginning of the game, the players send the position of their ships and their first shot to the Game Master. Ships positions will remain secret until the end of the game, while the first shot of both players will be displayed simultaneously; from this moment the game starts
  3. After each pair of shots has been displayed, each player must reply within 48 hours, sending the result of the opponent's shot. The player who will not reply in time, or who makes a calculation mistake, is disqualified and loses the game. The player who replies first scores one speed-point (see rule #6)
  4. After results have been displayed, each player must shoot again within 48 hours. The player who will not shoot in time is disqualified and loses the game. The player who shoots first scores one speed-point (see rule #6)
  5. Both players' shots and their results are always displayed together, at 2 o' clock p.m. (Rome time)
  6. The player who first sinks the opponent's fleet wins the game. If both fleets are sunk at the same time, the winner will be the player whose speed-score is higher


  7. rules' list







     





    General mathematical rules

  8. Intersections between straight shots and the fleet must be transmitted only if they are inside the battlefield. The co-ordinates must be rounded to integer values.
  9. The result of a conic shot can only be the sinking; i.e. if the conic is not sunk, no intersection must be transmitted.
  10. Line and conic equations must be always transmitted in implicit form; coefficients must be integer relative numbers
  11. Straight lines must be at an angle between 10° and 80° to the x-axis
  12. rules' list
















     



    Locating ships

  13.   Ships may overlap and intersect
  14.   Conics that factor into two lines are not allowed by international agreements
  15.   Ellipses
  16.   Parabolas
  17.   Hyperbolas
  18. rules' list





     



Skill levels

Depending on the skill level , fleet are constituted as follows:

rules' list