Pentopia

Rules

Shade some empty cells black so that the black cells form the shapes of different pentominoes. Each pentomino shape is used at most once, but can be rotated or reflected. Pentominoes cannot touch along edges or corners. Arrows in a cell indicate all closest shaded cell(s) to that cell along the four orthogonal directions (if there are multiple cells of the same closest distance to the cell, there will be multiple arrows).

(Rules and example from PGP IB)

History of the puzzle

Invented by Bram de Laat (Netherlands) in 2011. First appeared on LMI monthly test as a hybrid between Pentominoes and Myopia.

Variants

Twilight Pentopia

First appeared on WPC 2019/Round 8, "Twilight" round. The puzzle was by Gabi Penn-Karras.

Place some pentominoes into the grid, so that they do not touch each other, not even diagonally. Pentominoes can be rotated and reflected; no pentomino can be used more than once. Pentominoes can overlap cells with arrows.

If a cell containing one or more arrows is not part of any pentomino, the arrows indicate the directions of the nearest pentomino cells. If there is no arrow in a specific direction, then the nearest pentomino cell is farther away, or there may be no such cell in this direction at all.

If a cell containing one or more arrows is part of a pentomino, the arrows indicate the direction of the nearest cells that are not part of any pentomino. If there is no arrow in a specific direction, then the nearest cell that is not part of any pentomino is farther away, or there may be no such cell in this direction at all.

(Rules and example from WPC 2019 IB)

Appearances in the past WPCs

• WPC 2019/Round 8 (Pentopia, Twilight Pentopia) by Gabi Penn-Karras
• WPC 2019/Team Playoffs by Roland Voigt
• WPC 2019/World Cup Playoffs by Erhard Notz
• WPC 2017/Round 16 by Rajesh Kumar
• WPC 2016/Round 10 by Matej Uher