Any help is a great help.

Thanks

Gareth

I do not think it's fair to call a question to which you do not know a solution simple. This is what Fermat might have said about that problem of his that became known as the FLT.

A short answer to your question is that, No, not all combinations of starting and ending positions are solvable.

There exists a Rule of Two: a peg can only jump an even number of places in either direction.

There's also a Rule of Three: if we start with a single space and end up with a single peg, then it is possible to move in steps of three from the initial space to that of the final peg.