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:

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

Example

sum-star-examplesum-star-example-solution

Puzzles

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

PDF Sum Star

01. Medium

 sum-star-medium-01

02. Hard

sum-star-hard-02

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.

switches

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.

types-of-connections

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

kropki-switch-examplekropki-switch-example-solution

Puzzles

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

PDF Kropki Switch

01. Medium

 kropki-switch-01-medium

02. Hard

kropki-switch-02-hard

03. Expert

kropki-switch-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:

  1. 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.
  2. For every vertex touching exactly 3 cells, at least one cell must be unshaded.
  3. One must be able to draw a single loop through all shaded cells.

Example

rhombile-transparent-tapa-loop-examplerhombile-transparent-tapa-loop-example-solution

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

 rhombile-transparent-tapa-loop-medium-01

02. Hard

rhombile-transparent-tapa-loop-hard-02

03. Easy

rhombile-transparent-tapa-loop-hard-03

Killer Sudoku Hybrids

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.

Star Battle Killer

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.

star-killer-1

Butterfly X Nurikabe Killer

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.

butterfly-x-nurikabe-killer

Killer Battleships

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.

killer-battleship-sudoku

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

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

trapezoids-compound-r01-p01

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Round 2 – Simple Givens

Some shaded cells are given.

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

trapezoids-compound-r02-p01

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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

trapezoids-compound-r03-p01

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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

trapezoids-compound-r04-p01

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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.

trapezoids-compound-r05-exampletrapezoids-compound-r05-example-solution

trapezoids-compound-r05-p01

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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

trapezoids-compound-r06-p01

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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

trapezoids-compound-r07-p01

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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

trapezoids-compound-r08-p01

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