# Magic Snail

## Rules[edit]

Place a digit from 1 to N into some cells so that each digit appears exactly once in each row and column. Cells may remain empty. A cell cannot contain more than one digit. Along the path of the “snail” indicated by the bold lines (starting from the outside and going towards the center), the digits must start with 1 and be in consecutive ascending order, starting over from the highest digit to the lowest (that is, 1-2-..-N-1-2-..-N-1-2...). Some numbers and empty cells (marked with ‘X’) may be already filled in the grid.

(Rules (modified) and example (N=3) from PGP IB)

### Rule variations[edit]

**Magic Labyrinth**: Path is not a spiral. Named by Bernhard Seckinger in 2008.^{[1]}

## History of the puzzle[edit]

At least dates back to 2002. It was used as an assignment of a programming class in Budapest University of Technology.^{[2]} This fact vaguely suggests the puzzle's Hungarian origin, but it is not a certain fact.

## Variants[edit]

### Easy as Snail[edit]

Hybrid with Easy as clues. At least present in the 8th 24hPC (2007) ^{[3]} but possibly predates this.

Place given set of letters so that they follow Magic Snail rules. The letters around the grid denote the first letter visible from the given direction in the given row, column or diagonal.

(Example (1,2) from the 8th 24hPC IB)

#### Rule variations[edit]

- In
**Snail End View**on WPC 2018/Round 6, clues in a row referred to the second letter seen from that direction, no letters repeated on both diagonals and diagonal clues were also available. - In
**Snail End View Untouchable**on WPC 2018/Round 6, clues in a row referred to the second letter seen from that direction and there were No Touch restriction.

### Sky Snail[edit]

Invented by Rajesh Kumar (India) in 2010. ^{[4]} Hybrid with Skyscrapers clues.

Classic Magic Snail rules. In addition, the numbers represent heights of the buildings. The numbers around the grid indicate the number of buildings you can see from the given viewpoint.

(Rules (modified) and example from WPC 2018 IB)

### Magic Pathways[edit]

Invented by Christian Halberstadt (Germany) in 2014. His first puzzle can be seen on LMD portal.

Enter numbers from 1 to N into the grid, so that each number appears exactly once in each row, column and outlined region. Cells marked with a − cannot contain any numbers. Within each region, it must be possible to find a path that runs horizontally and vertically through each cell exactly once, including those marked as empty, and along the path the numbers from 1 to 4 appear in order. Such a path cannot cross bold lines. If a region has an entrance from the outside, the path must start at that entrance, and starting from that entrance the number 1 must appear first on the path.

(Rules (modified) and example (N=3) from WPC 2019 IB)

### Snail Odd/Even[edit]

First appeared on WPC 2018/Round 5. The puzzle was by Jiří Hrdina (Czech Rep).

Place given set of letters so that they follow Magic Snail rules. The cells marked with "E" may only contain even numbers. The cells marked with "O" may only contain odd numbers.

(Example (N=3) from WPC 2018 IB)

### Snail on Snake[edit]

Hybrid with Snake. First appeared on WPC 2018/Round 5. The puzzle was by Jiří Hrdina (Czech Rep).

Draw a snake. The numbers around the grid indicate the number of cells occupied by the snake in the corresponding row/column. Some of the snake cells are numbered, following the Magic Snail rule with 1 to N, seen from the head of the snake to the tail.

(Example (N=2) from WPC 2018 IB)

## Appearances in the past WPCs[edit]

- WPC 2019/Round 2 (Magic Pathways) by Christian Halberstadt
- WPC 2019/World Cup Round 3 by Gabi Penn-Karras
- WPC 2018/Round 2 (Sky Snail) by Jiří Hrdina
- WPC 2018/Round 5 (Snail Odd/Even) by Jiří Hrdina
- WPC 2018/Round 6 (Snail End View, Snail End View Untouchable) by František Luskač
- WPC 2018/Individual Playoffs (Snail End View Untouchable, unused) by František Luskač
- WPC 2013/Part 3 (Digital Snail)
- WPC 2013/Part 14
- WPC 2012/Part 8
- WPC 2011/Part 5
- WPC 2011/Part 11 (Sudoku Snail)