Pentalpha
Encyclopedia
Pentalpha is a puzzle
where the goal is to place nine stones on the ten intersections
of a pentagram
. The following rules need to be obeyed when placing the stones:
The solution to Pentalpha can be found for any starting point using the following algorithm
:
Puzzle
A puzzle is a problem or enigma that tests the ingenuity of the solver. In a basic puzzle, one is intended to put together pieces in a logical way in order to come up with the desired solution...
where the goal is to place nine stones on the ten intersections
Line-line intersection
In Euclidean geometry, the intersection of a line and a line can be the empty set,a point, ora line. Distinguishing these cases, and finding the intersection point have use, for example, in computer graphics, motion planning, and collision detection....
of a pentagram
Pentagram
A pentagram is the shape of a five-pointed star drawn with five straight strokes...
. The following rules need to be obeyed when placing the stones:
- The stone has to visit two other points before reaching its final point.
- These three points have to be next to each other.
- The points have to be in a straight line.
- The first and third (final) points are not allowed to be occupied, the second point is.
Solution
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
:
- Choose a node X.
- Travel two nodes in a straight line to node Y.
- From node Y, place a stone at node X.
- Let node Y be the new node X.
- Repeat step 2-4 until the puzzle is solved.
- Congratulations for completing it.