Friday, 16 December 2022

Freddie Hand

It's pentomino time! Did you know that out of the 12 pentominoes, 6 of them have a 3x3 bounding box and the 6 others have a 2xn bounding box? Unfortunately this fact probably won't be helpful for this Pentopia, where some of the pentominoes may be missing.

Rules: Shade some pentominoes of cells so that no pentominoes touch one another, not even diagonally. No two shaded pentominoes may be the same shape, counting rotations and reflections as the same. Clued cells cannot be shaded, and contain arrows indicating all of the orthogonal directions in which a shaded cell appears closest to the clued cell. At least one shaded cell must appear in the direction of an arrow.

To see the last part of the rules in action, examine R3C3 in the example solution. Going up and down, the nearest shaded cell is two away (the closest a shaded cell is to the clue); going right it is three away, and going left there is no shaded cell (effectively infinitely far). So the clue is satisfied. We could not shade e.g. R3C1 since that would also be 2 away from the clue, which would then need an additional left arrow. And indeed if we were to shade R3C2 the clue would need to be just a left arrow. I.e there is a "Negative Constraint" on clues!

Example, from puzz.link rules page (Puzz.link): https://tinyurl.com/3jbzfdc5

Note: The example puzzle uses the set of tetrominoes, not pentominoes! The rules are otherwise unchanged. And observe that not all shapes need to be used.

For a Speedy Sloth 🦥 solve in 3:45 or less!
For a Quick Crab 🦀 solve in 7:45 or less!
And all solvers who finish get a Blokus Banded Broadbill 🐦

Puzzle (Puzz.link): https://tinyurl.com/45rt87tp

If you're on a small screen, it may be preferable to use this version - https://tinyurl.com/mrys9226 - which has an extra column added to the right (so that the pentominoes fit on two rows). But make sure to permanently green the rightmost column!