Up to symmetry, there are 17 different one hole-one peg problems allowed by the parity counts. 12 can be done, 5 cannot.

Possible:

e1-e1, b4-e1, e5-e1, e3-e5, e1-e5, b4-e5, e5-e5,

e1-b4, b4-b4, e5-b4, b4-h4, e5-e3.Impossible:

e1-e3, b4-e3, e3-e3, e3-e1, e3-b4.

We will see later that the x-y problem is equivalent to the y-x problem.

In other words, doing e3-e5 is equivalent to doing e5-e3.

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