Racetrack (game)

Racetrack is a strategy game with pencil and paper of unknown origin for two or more players. It is also known under names such as car racing, formula Vector, Vector race, race box, Vector or Vector Rally Race, Graph racers, PolyRace, paper - and-pencil racing or the graph paper racing game. Racetrack is played on a checkered paper sheet (5 -mm mesh ). The game simulates a car race. Since the cars have a certain inertia, must be braked eg from a dangerous curve. For a successful game of the game therefore requires foresight and planning.

Base Game

Here the rules are explained in simple sentences. In a later section, when the mathematical concept of the vector is known, some of the rules may be formulated shorter.

On a checkered sheet of paper a closed line is drawn as outer boundary of the racetrack freehand. A large ellipse is sufficient to start with, but some irregularities make the game more interesting. Another closed line is drawn freehand within the first. You can more or less run parallel to the outer line, or the line may have wider or narrower (Eng ) sites, with usually at least two boxes between the lines. Somewhere between the two lines, a straight line is drawn. This is the start and finish line. You choose a direction for the race, for example counterclockwise.

The order of play is decided. Each selects a color or mark ( such as x or o ) representing the player's car. Each player draws a a starting point for his or her car - a grid intersection point on or behind the starting line.

It is said that each lattice point has eight neighbors, so that the eight lattice points are meant to be achieved when going up or down a box and / or a box to the left or right. Each train runs from the current grid point ( starting point ) to another grid point ( end point). The train is entered by a line is drawn from the starting point to the end point in each player's color. The new point gets chosen by the player marker ( eg, x or o). Players take turns.

As you drag, the following rules apply:

• The first train of each player must lead to one of the eight neighbors of the start point. The player also has the option to stand on its starting point.
• In any other train the so-called main point for this train is determined. The main point is obtained by repeating the previous train, both in horizontal and in vertical direction. If the player has recently pulled two boxes to the right and four box up, so the main point is now two boxes to the right and four above the current starting point. The player now has the option to draw directly to the main point or to one of its eight neighbors.
• The cars must remain within the distance limitations. This applies at every train for the starting point and the end point of the entire route, which connects both

The winner is the first player who completes one round ( cross the line ) has. The game is then terminated.

Additional and alternative rules

By combining the following rules in different results in countless variations of the game.

• Route The course must be no closed course; Start and finish lines may be different.
• Before the game, the players check the route and decide in advance whether a point near the edge of the track is inside or outside the track.
• Alternatively, the route may consist only of straight lines only 90 ° - 45 ° curves contain or exactly on grid points. Decisions on unclear route points are superfluous. Players can be allowed or forbidden to touch the edges, but not to exceed.

• Trains Instead of trains to each of the eight neighbors of the principal point to allow ( which can be reached in a Three Kings in the Western chess), you can use the four -neighbor rule and only allow trains to the main point and its four nearest neighbors ( the case of a Generalszug in Chinese be achieved chess).
• When drawing the route slippery areas are drawn as oil slick, where the cars, the speed can not change or only after the four -neighbor rule, this rule is applied for trains that start, for example, in the slippery region.

• Collisions and accidents The cars may be allowed to occupy the same point simultaneously. However, the rule most commonly used and most entertaining is that although themselves may overlap routes, but a car may not move onto a grid point or cross it when it is occupied by another car, as if the cars would collide.
• One can introduce a rule that requires that the player must try to avoid collisions. However, such a rule requires a certain interpretation.
• Another possibility is to punish collisions somehow, but it does not completely prohibit: Collisions can be defined, which is the driver "punished" with the higher speed is faster or slower than the other; the faster could again have to approach zero, whereas the slower must continue with previous speed.
• The slower riders could take the speed of the faster and faster must continue to travel at the speed of the slower one.
• Coming from behind " passes " its speed to the front; the latter may (or must - Beware of curves! ) continue correspondingly faster, while the rear has to move at zero again.

• A player who leaves the track, the continuation can be made possible in various ways, as long as he does not have to drop out or lose the win: The car must be decelerated to zero ( suspend one round and then along the course again approach ) or the route re-entered before the point of leaving and moving to there from scratch.
• The car is not braked, but must enter the course again, and, crossing the border stretch at one point, which is immediately before the point at which it left the track (usually requires an arc of several trains ).
• As a variant, in advance along the route " driveways " are referred to, and only about these entrances the route re-entering, the driver needs to back up to the next driveway.
• Furthermore, it needs outside of the course walking speed allowed (not per train faster than on a neighboring point), or even maintain the Geschwindikgeitsänderungsregel ( which might require a wide berth to the entrance ).

At high speed penalties require a considerable number of trains; other forms of punishment may be considering - the rule variations are limitless.

• Determining Victory At the end of the game, the current round must be completed. So, for example, of the three players A, B and C ( starting in this order), B reaches the first target, C must still run a train to a complete ABC anyway - complete cycle. The winner is the player whose car furthest crosses the finish line. Because - to stay with the above example - B may indeed be the first to reach the goal, but maybe it creates C even further over the finish line.
• If the above collision rule applied, it is no small advantage to draw first. This may be partially offset if the players choose their starting point in the reverse order. For example, C selects the start point first, then B, A. Then last makes the first train A, followed by B and C.
• Also alternating sequences are possible
• Another possibility is to let the losers in the next game first.

Mathematics and Physics

Each train can be represented by a vector. For example, a train two boxes to the right and four upwards can be represented by the vector (2,4). The eight -neighbor rule allows changing each coordinate of the vector by ± 1 If the previous train ( 2.4 ) was the next train to one of nine must be:

If each round represents a second and each box one meter, so does the vector for a train speed in meters per second. The four -neighbor rule allows an acceleration up to 1 meter per second squared, the eight -neighbor rule an acceleration up to √ 2 meters per second squared. ( Agreed to 10 meters per box instead, then the size of the track and the acceleration closer to reality. )

The speed caused by the acceleration can be reduced only at the same rate. This restriction reflects the inertia or momentum of the car. Note that in physics the speed record, the brakes or left- or right - turning all forms of " acceleration" are represented by a vector. For a sports car, it is not unrealistic to allow the same maximum acceleration in all directions.

Past and present

The origins of the game are unknown, it certainly existed in the 1960s, and it is reported that it was invented by engineers. Eugen Oker writes in his book on pencil and paper games, it had appeared in America " for the first time in a scientific journal ." If one considers the close connection to physics, that sounds credible. Today, the game of mathematics and physics teachers used throughout the world to teach vectors and kinematics. Anyway, the game has its own charm and some can be played for pure pastime.