Sink the conic!
Directions
Sink the conic is very similar to the game Battleships:
- the battlefield is a square with co-ordinates |x| <= 50 |y|
<= 50
- each player must place two conics (his ships) in his own field,
according to his skill level
- the aim is to locate the rival ships and sink them
- 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
- 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
- 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
- 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
- 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
- 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)
- 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)
- Both players' shots and their results are always displayed together,
at 2 o' clock p.m. (Rome time)
- 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
General mathematical rules
- 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.
- The result of a conic shot can only be the sinking; i.e. if the conic
is not sunk, no intersection must be transmitted.
- Line and conic equations must be always transmitted in implicit
form; coefficients must be integer relative numbers
- Straight lines must be at an angle between 10° and 80° to the
x-axis
Locating ships
- Ships may overlap and intersect
- Conics that factor into two lines are not allowed by international
agreements
- Ellipses
- must have semi-axes and center co-ordinates multiple of 5
- must have product of semi-axes not lower than 125
- must be interely located inside the battlefield
- may be circles
- Parabolas
- must have vertices whose co-ordinates are multiple of 5
- must have at least 2 intersections with the co-ordinate axes (inside
the battlefield)
- the distance between the vertex and the focus must be not lower than
1/8 and not greater than 25
- Hyperbolas
- must have vertices whose co-ordinates are multiple of 5
- must have vertices located within the region |x| <= 25, |y| <=
25
- the angle between the asymptotes must be not lower than 30° and
not greater than 150°
Skill levels
Depending on the skill level , fleet are constituted as follows:
- beginner: one ellipse and one parabola, with axes parallel to
co-ordinate axes
- intermediate: two conics of your choice, but of different types,
among ellipse, parabola and hyperbola, having axes parallel to co-ordinate
axes
- advanced: two conics of your choice, but of different types,
among ellipse, parabola and hyperbola, having axes of any slope