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Logicsmith Exhibition 7: Pentominous Borders (RESULTS!)

Four weeks ago, I challenged my readers to divide a 15x15 grid into as few regions as possible to create a valid Pentomonious Borders puzzle (that is, there is exactly one way to further divide the regions into pentominoes, regions of five cells each, so that no two congruent pentominoes, even if rotated or reflected, share an edge), with ties being broken in favor of which puzzle has the most faux solutions (that is, solutions where you disregard the rule that congruent pentominoes cannot share an edge). I received 6 entries, all of which managed to accomplish the task with just 2 regions! Their entries are collated below:
The winner, with 2 regions and over 13 billion faux solutions, is TheGreatEscaper! He will receive every puzzle in my Patron Puzzles for Philanthropy initiative! Additionally, Hugo van Rooigen, Bryce Herdt, and Michael Tang will receive all the digital puzzles from Patron Puzzles for Philanthropy! Congratulations!

2 comments

John Bulten said...

Hey Grant! These are really, I mean amazingly really, really lovely puzzles. Congratulations to everyone who succeeded and everyone who tried; my own thoughts on composition didn't even scratch the surface of what could be done.

How did you calculate the total solution count? Did you do them all by hand and/or get someone to double-check you? I haven't tried it by hand myself but I am wondering if there is an algorithm or app for that!

Grant Fikes said...

@John: I counted the solutions with a combination of Polysolver (https://www.jaapsch.net/puzzles/polysolver.htm), Windows Calculator, and figuring out by hand which areas were forced to be separate.

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