# List of Fillomino variants

There are a lot of Fillomino variants. *Fillomino-Fillia* 1 and 2 by Palmer Mebane and Grant Fikes were contests that consisted only of Fillomino variants.^{[1]}

### Nonconsecutive Fillomino[edit]

Appeared on Palmer Mebane's (USA) website in 2010.^{[2]}

Divide the grid into several regions, so that regions whose difference in size is less than 2 cells do not share an edge. Each number indicates the size of the region it is located in. Regions may contain none, one or several numbers.

(Rules (modified) and example from WPC 2017 IB)

### Kropki Fillomino[edit]

First appeared on 2010 German Qualifier. ^{[3]} Author of the puzzle was Florian Kirch (Germany).

Divide the grid into several regions, so that regions of the same size do not share an edge (they may touch diagonally). Each number indicates the size of the region it is located in. Regions may contain none, one or several numbers.

A black circle between two horizontally or vertically adjacent numbers indicates that one of these numbers is exactly twice the other; a white circle indicates that the difference between these numbers is exactly 1. If there is no circle between two adjacent numbers, none of these two properties may hold.

(Example from the IB for 2010 German Qualifier)

### Sum Fillomino[edit]

Appeared on Palmer Mebane's (USA) website in 2011 as a preview puzzle for Fillomino-Filia contest on Logic Masters India.^{[4]}

Divide the grid into several regions, so that regions of the same size do not share an edge. Each number indicates the size of the region it is located in. Regions may contain none, one or several numbers. Additionally, the grid contains some cages. The number at the top left of each cage gives the sum of all numbers that appear inside of it. Numbers may be repeated in cages.

(Rules (modified) and example from WPC 2017 IB)

### Queen Fillomino[edit]

Appeared on Prasanna Seshadri's (India) website in 2013.^{[5]}

Divide the grid into several regions, so that regions of the same size do not share an edge. Each number indicates the size of the region it is located in. Regions may contain none, one or several numbers. Additionally, all 1-cell polyominoes must be treated like queens in chess, i.e. no two queens, i.e. "1s", can see each other in any horizontal, vertical or diagonal line of cells.

(Rules (modified) and example from WPC 2017 IB)

### Symmetry Fillomino[edit]

First appeared in 2013 JZdC (a puzzle competition in Japan) under the name Tentai-sho Fillomino. Tentai-sho means "rotationally symmetrical" in Japanese and is a Japanese name for Spiral Galaxies. The author of the puzzle was Atsumi Hirose (Japan).

Divide the grid into several regions, so that regions of the same size do not share an edge. Each number indicates the size of the region it is located in. Regions may contain none, one or several numbers. Additionally, all regions must have rotational symmetry.

(Example from WPC 2016 IB)

### With a Given Set of Numbers[edit]

When the given set is {1, 2, 3}, the puzzle is widely known as **Trinudo**, named by Philipp Hübner (Germany) in 2012. This more general form, however, first appeared on WPC 2018/Round 5. The puzzle was by Jiří Hrdina (Czech Rep).

Divide the grid into several regions, so that regions of the same size do not share an edge. Each number indicates the size of the region it is located in. Regions may contain none, one or several numbers. Additionally, only regions with the given values as the area may be used.

(Example (1,2,3) from WPC 2018 IB)

#### Rule variations[edit]

- In
**Restricted Fillomino**from WPC 2017/Round 14, a set of numbers was not given. Instead, numbers already present in the unsolved grid were allowed.

### Regional Fillomino[edit]

First appeared on WPC 2018/Round 11, "Regional" round. The puzzle was by Jiří Hrdina (Czech Rep).

Divide the grid into several regions, so that regions of the same size do not share an edge. Each number indicates the size of the region it is located in. Regions may contain none, one or several numbers. Additionally, each outlined region contains the same set of numbers. Solvers must determine the set.

(Example from WPC 2018 IB)

### Pinocchio Fillomino[edit]

First appeared on WPC 2018/Round 13, "Twisted" round. The puzzle was by Jan Zvěřina (Czech Rep). This puzzle was inspired by Pinocchio Sudoku from WSC 2012.

Divide the grid into several regions, so that regions of the same size do not share an edge (they may touch diagonally). Each number indicates the size of the region it is located in. Regions may contain none, one or several numbers. Clues come in triplets of the same numbers. However, exactly one of the numbers in each triplet is wrong.

(Example from WPC 2018 IB)

## Appearances in the past WPCs[edit]

- WPC 2018/Round 5 (with a Given Set of Numbers) by Jiří Hrdina
- WPC 2018/Round 11 (Regional) by Jiří Hrdina
- WPC 2018/Round 13 (Pinocchio) by Jan Zvěřina
- WPC 2018/Individual Playoffs (With a Given Set of Numbers, Regional) by Jiří Hrdina
- WPC 2018/Individual Playoffs (Pinocchio) by Jan Zvěřina
- WPC 2017/Round 14 (Queen Fillomino) by Prasanna Seshadri
- WPC 2017/Round 14 (Nonconsecutive Fillomino) by Amit Sowani
- WPC 2017/Round 14 (with a Given Set of Numbers) by Deb Mohanty
- WPC 2017/Round 14 (Sum, Instructionless) by Rohan Rao
- WPC 2016/Round 2 (Symmetry) by Matej Uher
- WPC 2016/Round 3 (Kropki) by Matúš Demiger
- WPC 2016/Round 15 (with a Given Set of Numbers, part of a Matchmaker puzzle) by Matej Uher
- WPC 2016/Team Playoffs (Kropki) by Matej Uher

## References[edit]

- ↑ https://logicmastersindia.com/lmitests/?test=FF2
- ↑ https://mellowmelon.wordpress.com/2010/02/05/puzzle-183/
- ↑ https://logic-masters.de/LM/2010/dokumente/LM2010-Quali-Anleitung_en.pdf
- ↑ https://mellowmelon.wordpress.com/2011/06/02/puzzle-324/
- ↑ https://prasannaseshadri.wordpress.com/2013/01/23/puzzle-no-276-277-a-queen-sudoku-and-a-queen-fillomino/