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Wei Hwa's Puzzle Challenges #3

Here's a puzzle based on Erich Friedman's "Distance," from the 2003 Google U.S. Puzzle Championship. Label 14 of the circles above with different numbers from 1 to 14, such that the distance between 1 and 2 is less than the distance between 2 and 3, and so on. Four circles should remain empty.

Note that this image is not part of the solution but just an example.



See comments for solution.

Tags: Wei-Hwa, puzzle