``The method of undetermined generalization and specialization illustrated with Fred Galvin's amazing proof of the Dinitz conjecture'' (Appeared in the Amer. Math. Monthly, March 1996).

The Dinitz conj. became famous when Jeannette Janssen `almost' proved it, and was written up in Science Magazine (by Barry Cipra). Fred Galvin's complete proof, less than a year later, was a astounding in its simplicity. In the present paper, I console myself for not finding this proof myself, by playing a `pretend game': how I, and you, could have found this proof if we would have followed Hilbert's advice.

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My student John Noonan wrote some accompanying Maple programs.

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