Category: Kaleidoscope

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

Truncated Square Chocona

Chocona (チョコナ) is a puzzle type that likely originates with Nikoli.  I have adapted it to play on a Truncated Square grid.

Rules

Shade some cells such that:

  1. A filled square may not share an edge with a filled octagon.
  2. Filled octagons may share an edge, but only if the contiguous area of filled octagons forms a 45° oriented rectangle.
  3. Each bold-outlined region must have at least one filled octagon.
  4. Numbers indicate exactly how many cells, octagon or square, are filled in a bold-outlined region.  Regions with no number can have any number of filled cells.

Example

 Truncated Square Chocona ExampleTruncated Square Chocona Example Solution

Puzzles

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

PDF Truncated Square Chocona

01. Easy

Truncated Square Chocona Easy 01

02. Medium

Truncated Square Chocona Medium 02

03. Medium

Truncated Square Chocona Medium 03

04. Hard

Truncated Square Chocona Hard 04

05. Hard

Truncated Square Chocona Hard 05

06. Hard

Truncated Square Chocona Hard 06

07. Expert

Truncated Square Chocona Expert 07

Rhombitrihexagonal Yagit

Yagit (ヤギとオオカミ) is a puzzle type originally found in Puzzle Communication Nikoli volume 124 (September 2008).  I have adapted this puzzle to play on a Rhombitrihexagonal grid.

Rules

  1. Here is a field of sheep and wolves, represented by circles and triangles.  Draw some fences to divide the field into regions that each contain at least one sheep or one wolf, but not both.  No region can be empty.
  2. The fence must follow the path of a dodecagon, not turning more than 30 degrees at any vertex, unless it has a black dot.  Black dots indicate vertices where the fence may turn in any direction.  It is not necessary that a fence cross every black dot.
  3. Fences may not branch, but may intersect at any vertex that does not have a black dot.  Black dots can be part of at most a single fence.
  4. Fences must start and stop at the edge of the field.

Example

Rhombitrihexagonal Yagit ExampleRhombitrihexagonal Yagit Example Solution

Puzzles

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

PDF Rhombitrihexagonal Yagit Batch 1

01. Easy

Rhombitrihexagonal Yagit Easy 01.png

02. Medium

Rhombitrihexagonal Yagit Medium 02

03. Medium

Rhombitrihexagonal Yagit Medium 03

04. Hard

Rhombitrihexagonal Yagit Hard 04

05. Hard

Rhombitrihexagonal Yagit Hard 05

06. Expert

Rhombitrihexagonal Yagit Expert 06