One-Vacancy Problems

One-vacancy at e1

Suppose we start with one hole at e1, and we try end up with one peg. Where can that peg be? We already know that we can end up with one peg in e1, but can we end up with one peg anywhere else? The answer is yes, you can end up with one peg in either b4, h4, or e5. Can you figure out how to do this? It's really three different problems, but don't feel that you have to start all the problems from scratch.

Solution

One-vacancy at b4

If you start with one hole at b4, the possible ending spots are b4, h4, e1, and e5.

Solution

One-vacancy at e3

If you start with one hole at e3, the only possible ending spot is e5.

Solution

One-vacancy at e5

If you start with one hole in e5, the possible ending spots are e5, e1, e3, b4, and h4.

Solution

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