WLOG, x is one of e1, e3, e5, or b4. In other words,

you may assume that you start with one of

e1, e3, e5, or b4 empty.

Then the last peg must be in one of e1, e3, e5, b4, or h4.

However, this necessary condition is not sufficient.

For example, the e3-e3 problem satisfies this necessary

condition, but this problem has no solution.

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