### Rules

In addition to standard Kakuro rules, the grey shaded cells must form a valid Sudoku solution

### Puzzle

The puzzle can be found in this printable PDF, or in the image below.

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# Author: paramesis

## Sudoku embedded in a Kakuro

### Rules

### Puzzle

## Sum Star

### Rules

### Example

### Puzzles

#### 01. Medium

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#### 02. Hard

## Kropki Switch

### Rules

### Example

### Puzzles

#### 01. Medium

####

#### 02. Hard

#### 03. Expert

## Rhombile Transparent Tapa Loop

### Rules

### Example

### Puzzles

#### 01. Medium

####

#### 02. Hard

#### 03. Easy

## Killer Sudoku Hybrids

### Star Battle Killer

### Butterfly X Nurikabe Killer

### Killer Battleships

## Cairo Pentagonal Kurotto

### Rules

### Example

### Puzzles

#### 01. Medium

####

#### 02. Hard

#### 03. Hard

## Trapezoids Compound

# PDF Trapezoids Compound e-book

### Round 1 – Base Rules

### Round 2 – Simple Givens

### Round 3 – Unshaded Givens

### Round 4 – Row Counts

### Round 5 – XOR Dots

### Round 6 – XY Givens

### Round 7 – Interior Borders

### Round 8 – Obstructions

In addition to standard Kakuro rules, the grey shaded cells must form a valid Sudoku solution

The puzzle can be found in this printable PDF, or in the image below.

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.

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.

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

**PDF **Sum Star

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.

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.

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

**PDF Kropki Switch**

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.

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.

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

**PDF Rhombile Transparent Tapa Loop**

Over these last few weeks I’ve returned to my roots with a few Killer Sudoku variants, which I recently posted to the Daily League on Facebook. I have a few more ideas, but they’ll have to wait until after finals.

Place the numbers 1-8 and two stars in each row, column, and jigsaw group. Stars cannot touch each other, even diagonally. Numbers cannot repeat within cages. Stars count as 0 in cages.

This puzzle is made up of four overlapping 9×9 Sudoku grids arranged in a butterfly pattern (1 in each corner), each with it’s own set of main diagonals, which must contain the numbers 1-9. The sum/size of all cages are given, but not their shapes. The shapes of cages must form islands in a valid Nurikabe solution. Givens are shaded, and thus cannot be part of a cage.

Classic Sudoku rules apply. Additionally, a fleet of battleships must be placed into the grid, such that they do not touch, even diagonally. Cells occupied by the battleships must add up to the sum associated with each ship, and any cell sharing an edge with a ship cannot contain any of the numbers inside the ship. Numbers on the outside of the grid indicate how many cells in that row or column are occupied by a ship. Givens are “sea” squares, and cannot contain a ship.

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

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.

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

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:

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

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.

Some shaded cells are given.

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.

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.

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

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.

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.

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.