Playing Backwards-Examples

Diamond

This is an example we've already seen. The problem is to reduce the diamond to one peg at e1, and one solution is e1-g3, g3-c3, c3-e1.

The problem has solution e1-g3, g3-c3, c3-e1.

Here is the anti-problem. The anti-solution is c3-e1, g3-c3, e1-g3.

Moon over the Mesa

This is an example we've already seen. The problem is to reduce the diamond to one peg at e1, and one solution is e1-g3, g3-c3, c3-e1.

Moon-over-the-Mesa has solution b4-d2, h4-f2, e1-g3, g3-c3, c3-e1.

Here is the anti-problem. The anti-solution is c3-e1, g3-c3, e1-g3, h4-f2, b4-d2.

The e1-complement

If you take the anti-problem to a one-peg complement problem, you get the same problem. In other words, if you have a solution of a one-peg compelement problem, then taking the jumps in reverse order gives another solution.

Here is one solution: c3-e1, g3-c3, e1-g3, c5-e3, g5-c5, a5-e5, h4-f2, e5-g3, f2-h4, i5-g3, b4-d2, g3-c3, c3-e1.

The anti-problem is the same as the original problem, but the anti-solution is different: c3-e1, g3-c3, b4-d2, i5-g3, f2-h4, e5-g3, h4-f2, a5-e5, g5-c5, c5-e3, e1-g3, g3-c3, c3-e1. Note that the same peg makes the last three jumps.

Playing Backwards--Problems

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