Dijkstra’s Counting Arguments, Puzzles, and Cumulative Subgoal Fulfillment
Dijkstra’s Counting Arguments, Puzzles, and Cumulative Subgoal Fulfillment

Summary/Abstract: As Dijkstra and others have pointed out, puzzles can be an effective means for elucidating approaches to problem-solving. Dijkstra used puzzles to demonstrate the efficacy of arguments based on counting rather than on combinatorics. Using his and other puzzles, we show how the Cumulative Subgoal Fulfillment technique formalizes and extends Dijkstra’s approach. CSF is also used to solve the famous 15-puzzle theorem with a short, transparent proof.

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