The Perfect Game of Solitaire

Summary

A list of some of the principal requirements for a good game of solitaire would surely include:

1. I. The rules of the game should be few and simple.

2. II. The game should not require highly specialized equipment, so that it can be played almost anywhere and at almost any time.

3. III. It should be truly challenging.

4. IV. It should possess a number of interesting variations.

Judged by the above requirements, the Greeks of over 2000 years ago devised what can perhaps be considered a perfect game of solitaire—it might now be called the game of Euclidean constructions.

The rules of the game are given in the first three postulates of Euclid's Elements. These postulates read:

1. 1. A straight line can be drawn from any point to any point.

2. 2. A finite straight line can be produced continuously in a straight line.

3. 3. A circle may be described with any center and distance.

These postulates are the primitive constructions from which all other constructions in the Elements are to be compounded. Since they restrict constructions to only those that can be made in a permissible way with straightedge and compass, these two instruments, so limited, are known as the Euclidean tools.

The first two postulates tell us what we can do with a Euclidean straightedge; we are permitted to draw as much as may be desired of the straight line determined by any two given points.