in Bulgarian
An Abstract Strategy Game by Jordan Tuzsuzov

News :
19th August 2003 : New rule is added for preventing multiple usage of vectors. It can be used or not, depending the players.

Table of contents :

The game :

Veptheca is an abstract strategy game for two or more players, which is played with pen and paper or other surface (blackboard, indigo-board or even sand). The name of the game means Vector (int.) and Eptheca (addition, lat.). The main game rules are related to "connected vector", "vector" and "vector addition" in math.

Vector addition :

Very important knowledge for playing Veptheca is a rule for vector addition. The sum of vectors A and B is the vector C, which can be calculated with the following rule :

vector addition rule

Game rules :

The board of Veptheca is a square array of dots. The minimal size is 3x3 points, but bigger is better, for more strategy (I reccomend at least 4x4). Of course, for more than two players, bigger field must be used.
empty board
empty minimal playing-field 3X3.

Every player draws a vector on the field, with the following rules :

1. Horizontal or vertical vector, with length 1 (the distance, between two neighbour dots, in same line or column) with arbitrary direction, if the vector doesn't intersect any existing one.
2. Vector, whose is a sum of two existing connected vectors (non marked *), with joint vertex, if :
  • is a "discreet" (i.e. is drawn from dot to dot);
  • doesn't intersect existing vector;
  • must be joint with both vectors, whose sum is it (all 3 vectors must be joint, each to each);
  • for preventing multiple usage of already used vectors, mark the vectors, whose sum is it *.
The winner of the game, is the player, who makes the last possible move.
* This is a rule of multiple usage. The players can choose to play with or without it. I reccomend to play with this rule.

Examples of valid moves :
The game may look i little complex, but actually the rules are very simple. Here are some examples of VALID moves :

correct sum of two vectors

another correct sum of two vectors

one more correct vector - sum of two orthogonal vectors

This is a legal move with the latest game rules.

the longest blue vector is a sum of the two red vectors

Examples of invalid moves :
Here are some samples of INVALID moves in the game - the GREEN vector shows the invalid move :

the green vector intersects the existing blue vector.

the green vector is a sum of the blue and red vector, but only in math. In Veptheca, source vectors must have joint vertex.

another incorrect move in Veptheca - the sum vector doesn't have joint vertex with the first vector.

Game example :

These are animations, which shows a sample games on a minimal playing-field (3X3) for two players. The moves are in different colors just for clarity. The red player begins the game :

Sample game with the rule of multiple usage.

sample game animation
Sample game without the rule of multiple usage.

This game, the rules and the name, are copyright of Jordan Tuzsuzov.
Copyright Jordan Tuzsuzov, 2003