- What happens if we change the rules so that diagonal jumps are allowed as well?
- What happens if we use different shapes for the board?
- Can every reversal problem be solved?
- Instead of trying to get down to a single peg, suppose the purpose is to have as many pegs remaining as possible when no more moves can be made?
- Can we find interesting examples of two positions where it is possible to prove that no sequence of legal moves converts the first into the second position?
- Can we determine whether a position could have resulted from a give starting position.
- If we start with one open square and get down to one peg, where must that per be?