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:

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

Example

cairo-pentagonal-kurotto-examplecairo-pentagonal-kurotto-example-solution

Puzzles

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

PDF Cairo Pentagonal Kurotto

01. Medium

 cairo-pentagonal-kurotto-medium-01

02. Hard

cairo-pentagonal-kurotto-hard-02

03. Hard

cairo-pentagonal-kurotto-hard-03

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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.

trapezoids-compound-r01-exampletrapezoids-compound-r01-example-solution

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Round 2 – Simple Givens

Some shaded cells are given.

trapezoids-compound-r02-exampletrapezoids-compound-r02-example-solution

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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.

trapezoids-compound-r03-exampletrapezoids-compound-r03-example-solution

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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.

trapezoids-compound-r04-exampletrapezoids-compound-r04-example-solution

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Round 5 – XOR Dots

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

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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.

trapezoids-compound-r06-exampletrapezoids-compound-r06-example-solution

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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.

trapezoids-compound-r07-exampletrapezoids-compound-r07-example-solution

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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.

trapezoids-compound-r08-exampletrapezoids-compound-r08-example-solution

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Proximity Snake

This is an adaptation of various Snake types to a [3.4.6.4; 33.42] tiling.

Rules

Draw a snake through cells between the two given ends such that:

  1. The snake does not branch or cross itself.
  2. The snake does not touch itself on an edge.  If two cells that share an edge are part of the snake, the snake must be passing through that edge. The snake can touch itself on a vertex (“diagonally”).
  3. Numbers in certain cells indicate how many of the cells that share a vertex with the numbered cell are occupied by the snake.  The snake cannot pass through numbers.

Example

Dodecagon Square Joint Proximity Snake ExampleDodecagon Square Joint Proximity Snake Example Solution

Puzzles

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

PDF Proximity Snake

01. Easy

 Dodecagon Square Joint Proximity Snake Easy 01

02. Medium

Dodecagon Square Joint Proximity Snake Medium 02

03. Hard

Dodecagon Square Joint Proximity Snake Hard 03

Deltoidal Trihexagonal Tree

This type is an adaptation of Branch (ブランチャー) by Inaba Naoki to a Deltoidal Trihexagonal grid.

Rules

Draw segments to create a network such that:

  1. Every vertex • and node O is connected.
  2. Vertices must connect to exactly two path segments.  Every branch of the network must form a path from one node to another.
  3. Numbers indicate the sum of the lengths of every branch directly connected to that node, in segments.
  4. The network is acyclic – there are no loops.

Example

Deltoidal Trihexagonal Tree ExampleDeltoidal Trihexagonal Tree Example Solution

Puzzles

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

PDF Deltoidal Trihexagonal Tree

01. Medium

 Deltoidal Trihexagonal Tree Medium 01

02. Hard

Deltoidal Trihexagonal Tree Hard 02

03. Expert

Deltoidal Trihexagonal Tree Expert 03

Killer Tetrakis Square

Here is a type that borrows some constraints from Aziz Ates’ Triangular Skyscrapers puzzle in the 2016 US Puzzle Championship practice test.   The result is a close cousin of my specialty, Killer Sudoku, so I’ve made these puzzles harder than normal.

Rules

Fill numbers into the grid of four rows and four columns of 8 cells each such that:

  1. Every row and column contains each integer from 1 to 8 exactly once.
  2. Cages, represented by dotted lines, indicate the sum to which all included cells must add.
  3. Numbers may not repeat within a cage
  4. Each number must appear exactly once in each of the four triangle orientations (pointing NE, NW, SE, SW)  All of the “1” cells are highlighted in the example answer to demonstrate this.

Example

Killer Tetrakis Square ExampleKiller Tetrakis Square Example Solution

Puzzles

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

PDF Killer Tetrakis Square

01. Medium

 Killer Tetrakis Square Medium 01

02. Hard

Killer Tetrakis Square Hard 02

03. Hard

Killer Tetrakis Square Hard 03

04. Expert

Killer Tetrakis Square Expert 04

05. Expert

Killer Tetrakis Square Expert 05

Trapezoids

Here is a new type loosely inspired by Inaba Naoki’s Cell-Land.

Rules

Shade some cells such that:

  1. Numbers indicate exactly how many surrounding cells are filled.
  2. Filled cells must be in clusters of 3, forming trapezoids.  A trapezoid may not share an edge with another trapezoid.
  3. All unfilled cells are connected edge-to-edge.

Example

Hidden Trapezoids ExampleHidden Trapezoids Example Solution

Puzzles

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

PDF Trapezoids

01. Easy

Hidden Trapezoids Easy 01.png

02. Medium

Hidden Trapezoids Medium 02

03. Medium

Hidden Trapezoids Medium 03

04. Hard

Hidden Trapezoids Hard 04

05. Hard

Hidden Trapezoids Hard 05

06. Hard

Hidden Trapezoids Hard 06

07. Expert

Hidden Trapezoids Expert 07