# WPC 2019/Round 13

Duration: 75 minutes. Total point value: 3000 points. Round winner: JPN-A (Ken Endo, Kota Morinishi, Yuki Kawabe, Hideaki Jo), 4000 points.

### Puzzles[edit]

All puzzles in this round were written by Erhard Notz.

This puzzle can be seen as a successor to Geisterbahn series from German Nationals, mixed with Matchmaker elements.

This round consists of eight separate puzzle grids that are part of one large puzzle. Each grid has different rules. The task is to determine which rules belong to which grid, and solve the resulting puzzles.

The following general rules are valid for all eight puzzle grids: Draw a closed loop into the grid that runs horizontally and vertically. The loop must pass through all cells with circles and numbers. The loop may cross itself (unless this is prohibited by a special rule for an individual grid), but not in cells with circles; aside from that, no cell can be visited more than once. No crossings or unused cells are given.

There are additional rules in seven categories. Each grid must conform to exactly one rule from each category, and each rule must apply to exactly two grids. To find out which rules are assigned to each grid is part of the puzzle.

The rules the following:

#### Category 1: General - Global Rules[edit]

This category contains rules about global properties, namely restrictions on crossings and unused cells.

- The loop must pass through all cells.
- Each row and column must contain at least one cell that is not used by the loop.
- The loop cannot cross itself.
- The loop must cross itself at least once, but cells with crossings cannot touch each other, not even diagonally.

#### Category 2: Numbers Left – Segments[edit]

This category deals with clue numbers on the left side of the grid. These clues refer to horizontal loop segments in the respective row. A line connecting two adjacent cells is defined as length 1.

- Each clue number indicates how many separate horizontal loop segments appear in the respective row.
- Each clue number indicates the length of the longest loop segment in the respective row.
- Each clue number indicates the length that appears most often in the respective row. No other length can appear the same number of times.
- Each clue number indicates a length that is not found in the respective row.

#### Category 3: Numbers Above – Crossings[edit]

This category deals with clue numbers above the grid. There are exactly three such clue numbers in each grid. These clues indicate the number of crossings in the respective column. However, not all of these numbers are correct.

- All three clue numbers are correct.
- Exactly two clue numbers are correct
- Exactly one clue numbers are correct
- None of the clue numbers is correct.

#### Category 4: Numbers Inside – Geradeweg[edit]

This category deals with clue numbers inside the grid. These numbers are Geradeweg clues. However, some clues are Knapp Daneben. If the loop makes a turn or crosses itself in a Knapp Daneben clue number, the horizontal and vertical loop segments may have the same or different length.

- All clue numbers indicate the correct length (no Knapp Daneben). The loop may pass straight through, turn or cross itself in a clue cell.
- All clue numbers are Knapp Daneben, and the loop must pass

straight through all clue cells without crossing itself there.

- All clue numbers are Knapp Daneben, and the loop must make a turn in all clue cells.
- All clue numbers are Knapp Daneben, and the loop must cross itself in all clue cells.

#### Category 5: Circles – Masyu[edit]

This category deals with circles inside the grid. Some circles have Masyu properties. Some circles have neither property, they are not valid Masyu circles of either colour.

- All circles are white Masyu circles.
- All circles are black Masyu circles.
- All circles are neither white nor black Masyu circles.
- All circles are white or black Masyu circles, and along the loop white and black circles alternate (the loop never passes through two circles of the same colour consecutively).

#### Category 6: Arrows – Myopia[edit]

This category deals with diagonal arrows inside the grid. These clues are Myopia-like arrows. From each grid point with one or more arrows, these arrows point to the nearest cells in the four diagonal directions that have a certain property. If there is no arrow in a specific direction, then the nearest cell with the specified property is farther away, or there may be no such cell in the given direction at all.

- The arrows point to the nearest cells in the four diagonal directions where the loop crosses itself.
- The arrows point to the nearest cells in the four diagonal directions where the loop passes straight through.
- The arrows point to the nearest cells in the four diagonal directions where the loop makes a turn.
- The arrows point to the nearest cells in the four diagonal directions that are not used by the loop.

#### Category 7: Grey Regions – Symmetry[edit]

This category deals with grey regions. All such regions are 2×2 squares. Each such region must have an axis of symmetry. Aside of this, there are no restrictions on the loop; grey regions may contain crossings and unused cells, even completely empty regions are allowed. Symmetry refers only to the loop, not to additional elements (circles, arrows, numbers).

- In all regions, the axis of symmetry must run horizontally.
- In all regions, the axis of symmetry must run vertically
- In all regions, the axis of symmetry must run diagonally, from top left to bottom right.
- In all regions, the axis of symmetry must run diagonally, from bottom left to top right.

### Partial Scoring[edit]

Teams receive points for correctly identified rules. Every correct letter is worth 40 points, and every correctly solved puzzle is worth 90 points. However, if there are more than two letters below an icon, these letters will yield 0 points, even if one or two of them are correct. Similarly, if a letter appears below two icons in the same category, this letter will yield 0 points in this category, even if it is entered below the correct icon.