Divide the grid into polyomino-shaped regions such that each cell is in exactly one region. You may only draw on the grid, as indicated by the dotted lines. Each region must be rotationally symmetric and contain exactly one dot at the point of symmetry.
(Rules and example from PGP IB)
History of the puzzle
First appeared on Nikoli volume 96 (2001). Invented by ゲサク ("Gesaku"). Original title was 天体ショー ("Tentaisho," namely "Celestial Show"), which is a pun on 点対称 ("Tentaishou," namely "point symmetry").
Invented by Rohan Rao (India). First appeared on WPC 2017/Round 20.
Divide the grid into 180° symmetrical regions along the gridlines. Each region must contain exactly one circle, which represents the central symmetry point of the region. All circles are given. Some cells may not be part of any region. All the used cells must together form a single connected area that is 180° symmetrical.
(Rules and example from WPC 2017 IB)
Galaxies and Pentominoes
Place the twelve pentominoes into the grid so that they do not touch each other, not even diagonally. Numbers below and to the right indicate the number of cells used by the pentominoes in the respective row and column. Pentominoes may be rotated and reflected. Divide the remaining cells so that each region is rotationally symmetric and contain exactly one dot at the point of symmetry.
(Example (using 4 pentominoes) from WPC 2018 IB)
Appearances on past WPCs
- WPC 2019/Round 2 by Silke Berendes
- WPC 2019/World Cup Playoffs by Silke Berendes
- WPC 2018/Round 6 (Galaxies and Tetrominoes, Galaxies and Pentominoes) by Jiří Hrdina
- WPC 2018/Round 8 by Jiří Hrdina
- WPC 2018/Individual Playoffs (Spiral Galaxies (broken and replaced), Galaxies and Tetrominoes) by Jiří Hrdina
- WPC 2017/Round 9 by Rakesh Rai
- WPC 2017/Round 20 (Spiral Galaxies2) by Rohan Rao
- WPC 2016/Round 14 (part of a Permaculture hybrid) by Matúš Demiger
- WPC 2016/Age Division Playoffs by Martina Prinerová
- WPC 2013/Part 6 (Spiral Galaxies, Doubled Spiral Galaxies)
- WPC 2013/Part 7
- WPC 2013/Part 12