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Logicsmith Exhibition 8: [SPOILERS FOR WORDY WEDNESDAY 341]

WARNING: THIS CONTEST CONTAINS SPOILERS FOR WORDY WEDNESDAY 341, "THE OMINOUS PENTHOUSE 2"!!!

Wordy Wednesday 341 revolves around a single grid which can be solved as two separate logic puzzles. Specifically, it can be solved as a Pentominous (divide the white cells into pentominoes, regions of five cells each, so that no two congruent pentominoes, even if rotated or reflected, share an edge) and as a Battlestar (place stars in some of the white cells so that there are two stars in every row and two stars in every column, and so that no two stars are in cells which share an edge or a corner).
Inspired by this puzzle, I hereby issue my readers two challenges:

Part 1: Shade in some cells in a 10x10 grid so that the grid solves uniquely both as a Pentominous and as a Star Battle. Maximize the number of solutions the Pentominous would have if you disregard the rule that congruent pentominoes cannot share an edge. (You may find a program like PolySolver by Jaap Scherphuis to be helpful for counting such "faux solutions".) Your entry for Part 1 will not be accepted unless it has more than 96 faux solutions, the number of faux solutions the puzzle from WW341 has. Ties will be broken by random draw. The winner will receive a copy of my board game Mammalath (with the Mammalath Plus expansion).

Part 2: Same as Part 1, but all white cells must constitute the interior of a single simple polygon with no holes in it, as is consistent with the standard presentation of a Battlestar puzzle. Maximize the number of faux solutions to the Pentominous. I've written a puzzle for Part 2 just to prove that it's possible, and will showcase it after the deadline, but your entry will be accepted regardless of how many faux solutions it has (even if it's fewer than mine). Ties will be broken by random draw. As in Part 1, the winner will receive a copy of my board game Mammalath (with the Mammalath Plus expansion). Note: if the winners of Part 1 and Part 2 are the same person, I reserve the right to award the prize for Part 2 to second place instead.

You may enter either Part 1, Part 2, or both. Submit your puzzle(s) to glmathgrant[at]gmail[dot]com within the next 3 weeks (before 11:59 PM Central time on August 30, 2020). You may enter multiple times; only your best valid entry for each part will be counted. I will feature the best valid entries from every entrant on this blog, so even if you don't win, your puzzle-writing abilities will be showcased. Good luck!

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