Peg Solitaire is a single-player board game played on a board that has a pattern of holes or pegs. The standard board has 33 holes arranged in the shape of a cross with a hole in the center. The game is played by jumping one peg over another, removing the jumped peg and continuing until no more moves are possible.

The objective of the game is to remove as many pegs as possible, ideally leaving only one peg in the center hole. If you can achieve this, you have won the game. However, the game can also be considered won if you have removed a certain number of pegs, such as leaving only four pegs in the corner of the board.

Peg Solitaire is believed to have originated in France in the 17th century, and has since become a popular game around the world. There are many variations of the game, with different board sizes and patterns, as well as different rules and objectives.

A thorough analysis of the game is known. This analysis introduced a notion called pagoda function which is a strong tool to show the infeasibility of a given, generalized, peg solitaire, problem. A solution for finding a pagoda function, which demonstrates the infeasibility of a given problem, is formulated as a linear programming problem and solvable in polynomial time.

A paper in 1990 dealt with the generalized Hi-Q problems which are equivalent to the peg solitaire problems and showed their NP-completeness. A 1996 paper formulated a peg solitaire problem as a combinatorial optimization problem and discussed the properties of the feasible region called 'a solitaire cone'. In 1999 peg solitaire was completely solved on a computer using an exhaustive search through all possible variants. It was achieved making use of the symmetries, efficient storage of board constellations and hashing. In 2001 an efficient method for solving peg solitaire problems was developed. It can be proved using abstract algebra that there are only 5 fixed board positions where the game can successfully end with one peg.

I modified the Peg Solitaire Game to be played in a 4 by 4 board with 10 pegs. Below are some solvable samples.

QUESTION I : How many position one needs to study to solve English Peg Solitaire?
QUESTION II : Remove pegs in turn till possible. Could this be a viable modification for a couple to play?

REFERENCE : ChatGPT, Wikipedia