Tuesday, August 15, 2023

Puzzle #576 - Tapa (Line)

Serkan posed a challenge to create a 10x10 Tapa Line (Tapa rules + 4 shaded cells in a row is banned) puzzle with as large of an empty space as possible. After the obvious degenerate case of a single shaded cell clued with just one row and column, a couple people tried making serious puzzles. An 8x8 empty middle was found pretty quickly, but I felt 8x9 would be possible. And it was.

The tiebreaker was to be the lowest sum of clues, so a few values are lower than they otherwise need to be. I also showcased a degenerate case that would allow for an arbitrarily large empty region on arbitrarily large grids, even with the constraint that every row and column must have a shaded cell. Really, there is no good formulation of an optimization challenge like this that doesn't end up with a degenerate puzzle allowed!

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