The Kaleidoscope competition is returning to Logic Masters India this weekend! It will feature 14 new puzzles from the past 7 Kaleidoscope types, and will take place from 10/19 to 10/22, starting in a couple hours. See the instruction booklet and discussion forum by clicking the image or link below.

# Category: Kaleidoscope

## Omni-Yajilin

My first Nikoli puzzle book was Pencil Puzzle Yajilin 1, back in 2006 when the Pencil Puzzle series was available. Yajilin has always been a special puzzle type for me. It marks the beginning of that unscratchable itch that I think most puzzlers have, to relentlessly explore new puzzle types and variations and to engage with problems for which no well-trodden inventory of techniques already exists. I’m happy to return from my break with a Yajilin variation on a new tiling [33434; 3^{2}6^{2}; 3446; 6^{3}].

EDIT: Following a suggestion from edderiofer, I have made the clue cells easier to distinguish.

EDIT 2: Puzzle number 3 has been corrected. The far right hexagonal clue should have been a 3.

### Rules

Shade some cells and draw a loop in remaining cells such that:

- Every empty cell is either shaded or part of a single loop that does not branch or intersect.
- Numbers in some cells indicate the total number of shaded cells that can be seen in all directions from that cell. Lines of sight run perpendicular to the edges of a cell and terminate on the edge of the grid or at a triangular cell, counting that cell.

### Example

### Puzzles

All of the puzzles can be found organized in this printable PDF, or in the images below.

**PDF Omni-Yajilin**

#### 01. Medium

#### 02. Hard

#### 03. Medium

## Hexagonal Kurokuron

Kurokuron (クロクロ一ン: “black clone”), is a shading puzzle that first appeared in Puzzle Communication Nikoli issues 153-155. Identical rules apply to a hexagonal grid.

### Rules

Shade some cells such that:

- Bold-outlined regions contain exactly two shapes, made up of contiguous groups of 1 or more shaded cells. Within a region, the two shapes must be congruent, allowing reflection and rotation.
- A shape cannot share an edge with another shape.
- Cells with arrows, which cannot be shaded, point to a neighboring cell, which must be shaded and part of a shape consisting of the given number of cells.

### Example

### Puzzles

All of the puzzles can be found organized in this printable PDF, or in the images below.

#### 01. Easy

#### 02. Medium

#### 03. Medium

## Karst

### Rules

Variant of Cave:

- Draw a single loop along the dashed lines that encloses some cells. Edges of this loop may not cross or share a vertex.
- Numbers indicate the number of connected cells from all lines of sight radiating from that cell, including the cell itself. Numbers can be inside or outside of the loop. Lines of sight end on either the edge of the grid, the center of a triangular cell, or the edge of the loop.

### Example

### Puzzles

All of the puzzles can be found organized in this printable PDF, or in the images below.

**PDF Karst**

#### 01. Medium

#### 02. Hard

#### 03. Hard

## Sum Star

Here’s a type that came together in my notebooks back in October 2016. It’s nearest rectangular precedent is Gapped Kakuro by Serkan Yürekli. A puzzle of this type will be featured today on Grandmaster Puzzles.

### Rules

Fill cells with numbers and shade all remaining cells such that:

- Each dodecagon contains the numbers 1-9 exactly once.
- Numbers in cells sharing a vertex with a black triangle add up to the indicated sum without repeating.
- A shaded cell cannot share an edge with another shaded cell.

### Example

### Puzzles

All of the puzzles can be found organized in this printable PDF, or in the images below.

**PDF **Sum Star

#### 01. Medium

#### 02. Hard

## Kropki Switch

This may be the most obscure puzzle idea I’ve come up with yet. Even though it’s hard to explain, I like how it solves.

### Rules

Place the numbers 1-9 so that they appear exactly once in each 3×3 block of square cells.

Standard Kropki rules apply to borders between square cells:

- A black dot on the border between two square cells indicates that the ratio of those cells is exactly 2. A white dot on the border between two square cells indicates that the difference between those cells is exactly 1. A border between two square cells with no dot indicates that neither of these properties applies. (The border between “1” and “2” could have either a black or a white dot.)

Between the 3×3 blocks of square cells are switches, which consist of 3 triangles and 1 hexagon.

Exactly one cell from each switch must be shaded (for double switches, one cell from each side must be shaded). Shaded cells cannot share an edge. A switch relates triplets from different 3×3 blocks in the following three possible combinations: one triangle, one hexagon, or two triangles.

If the switch cell (or one of the two cells in the case of two triangles) is shaded, both triplets must contain the same three numbers. If the cell (or both cells in the case of two triangles) is unshaded, both triplets must contain different numbers. If a switch cell containing a number is shaded, any triplets touching that cell must contain that number. If the cell is unshaded, any triplets touching that cell must not contain that number.

### Example

### Puzzles

All of the puzzles can be found organized in this printable PDF, or in the images below.

**PDF Kropki Switch**

#### 01. Medium

#### 02. Hard

#### 03. Expert

## Rhombile Transparent Tapa Loop

Here is a transparent variation of Tapa-Loop by Serkan Yürekli adapted to a Rhombile grid. Some puzzles of this type crafted by Serkan and Fatih Kamer Anda will be featured on the upcoming Tapa Variations Contest hosted by Logic Masters India.

### Rules

Shade some cells such that:

- For any cell with one or more numerical clues, shaded cells form connected groups of the indicated size within the group of cells sharing a vertex with the clued cell. Cells with clues
**can**be shaded. - For every vertex touching exactly 3 cells, at least one cell must be unshaded.
- One must be able to draw a single loop through all shaded cells.

### Example

### Puzzles

All of the puzzles can be found organized in this printable PDF, or in the images below.

**PDF Rhombile Transparent Tapa Loop**

#### 01. Medium

#### 02. Hard

#### 03. Easy

## Cairo Pentagonal Kurotto

Here is an adaptation of Nikoli’s Kurotto to a Cairo Pentagonal grid.

### Rules

Standard Kurotto Rules. Shade some cells such that:

- Each circled number equals the total number of cells in all edge-connected clusters touching that cell.
- Cells with circles cannot be shaded.

### Example

### Puzzles

All of the puzzles can be found organized in this printable PDF, or in the images below.

#### 01. Medium

#### 02. Hard

#### 03. Hard

## Trapezoids Compound

I’m happy to announce my first e-book release on this blog! I borrowed an idea from David Millar, whose Area 51 puzzles combine clues from Slitherlink, Fences, Cave, and Masyu. I wanted to see how far I could take this idea, layering as many types of clues as I could into one of my own puzzles.

This collection of 20 puzzles introduces 8 different types of clues and explores how they interact with each other. Most of these puzzles are Hard to Expert difficulty, so expect a challenge. If you would like some easier puzzles to start out on, check out the original Trapezoids post from June.

Here is the e-book in pdf form laid out and formatted to letter size:

# PDF Trapezoids Compound e-book

The content of the e-book in blog form follows, except the solutions.

### Round 1 – Base Rules

Standard Trapezoids rules:

Shade some cells such that numbers indicate exactly how many surrounding cells are shaded. Shaded cells must be in edge-connected clusters of 3, forming trapezoids. A trapezoid may not share an edge with another trapezoid. All remaining unshaded cells are connected edge-to-edge.

### Round 2 – Simple Givens

Some shaded cells are given.

### Round 3 – Unshaded Givens

Cells with single or double circles must be unshaded, and thus must be connected to the remaining unshaded cells. Cells with a single circle must be touching exactly one shaded cell. Cells with a double circle must be touching exactly two shaded cells.

### Round 4 – Row Counts

Numbers on the outside edge of the grid indicate the total number of shaded cells in the indicated row. Only shaded cells, including givens, are counted.

### Round 5 – XOR Dots

Dots on the border between two cells indicate that one cell is shaded and the other is not.

### Round 6 – XY Givens

Some shaded cells are given, marked with an X or Y. **EITHER** all of the cells with an X have one neighboring shaded cell and all of the cells with a Y have two neighboring shaded cells **OR** all of the cells with an X have two neighboring shaded cells and all of the cells with a Y have one neighboring shaded cell.

### Round 7 – Interior Borders

Trapezoids cannot cross interior borders. The interior borders create regions, each of which must have at least one shaded cell. Interior borders do not block unshaded cells from connecting.

### Round 8 – Obstructions

Large black dots inside of a cell represent obstructions, which block unshaded cells from being connected. Additionally, obstructions cannot “see” each other; in any row of cells in which there is more than one obstruction, at least one of the cells between them must be shaded. Just like in row counts, a row of cells is either 0° (horizontal), 60° or 120°. Obstructions must be connected to the mass of unshaded cells. Obstructions are not counted in row counts.