Puzzlerium Tour: Irregular Hex Slitherlink

Although the puzzle is on a smaller, if not much smaller, than usual hex grids, I hope that the theme does not lose itself in the solve. Nothing remarkable is happening in this puzzle except for the theme, which is really why I am publishing this puzzle. On hex grids, Slitherlink works in a tad different way, in that, each cell has 2 more surrounding edges, and consequently a few more neighbors than in square grids. Secondly, as there are only 3 grid edges meeting at a point, there is really no possibility of two different subsections of the loop "meeting at a point" - usually a very useful meta logic in square grids to see that the move is wrong. 

Rules: Draw a single closed loop by connecting neighboring grid points along the grid lines. Each numbered cell or irregular group of cells indicates how many of its bounding edges are used by the loop.

About HexSlithehrlink:  Slitherlink was invented by Nikoli puzzles. Several of its variations have been explored since, some of them being Hex, Sheep and wolves, False clue, Polygraph, Irregular and more.

    

Puzzlerium Tour: Estate Lawns

Rules: Shade in some cells, so that all of the unshaded cells form a single region of contiguous cells. Numbers in bold outlined regions indicate how many blocks of contiguous unshaded cells (including unit cell blocks), ignoring unshaded cells in other regions, are in that region. Such unshaded cell blocks in different regions cannot be of the same size when they are touching each other orthogonally through region borders.

About Estate Lawns: Invented by Anurag Sahay, Estate Lawns debuts with the above puzzle. 

    

Puzzlerium Tour: Perfectland

Perfectland is as much a region division puzzle as it is a path puzzle. I reckon it comes closest to "Cave" in its feel. Instructions get slightly on the longer side, but it is only comforting that some Nikoli puzzles have instructions that are longer than this.

Rules: 

1.The grid contains symbols of three kinds, each representing living spaces. The task is to divide the grid along the gridlines into regions that enclose exactly one instance of each of the three symbols, so that a straight line path can be drawn in each region that visits each of the symbols without having to branch out, and starts and ends in one of the symbols. Some region borders may already be given.

2. No region may fully enclose any 2x2 areas of cells. In each region, there must be at least one cell not visited by the path (representing unused areas), and all such cells in the entire grid must be connected in a single group.

3. Unused cells cannot be scattered within a region - all of the unused cells in a given region must be connected in a single group. 

About Perfectland: Invented by Anurag Sahay, Perfectland was first published in 2020 (see example below to better understand how it works). 

    

Puzzlerium Tour: Pentapa

I don't enjoy constructing any Tapa variant as much as Pentapa or Tapa Logic, both of which were some of the earliest of Tapa variants known to be explored. This exquisite Pentapa works on a brilliant deduction around a single shape.

Rules: Paint some squares to create a continuous wall of connected cells. Number(s) in a cell indicates how many painted cells are contained in a continuous black cell block in its surrounding cells. If there is more than one number in the cell, there has to be at least one white cell separating the black cell blocks. Painted cells cannot form a 2x2 cell. Numbered cells cannot be painted. It must be possible to find all the pentomino shapes, without repetition, using only the painted cells, every painted cell used by exactly one shape. There cannot be any painted cell that is not part of any Pentomino. 

Puzzlerium Tour: Pento-Go-Round

Pentominous was perhaps the best of region division puzzles introduced this decade. The puzzle I am introducing here draws upon Pentominous. 

 

Rules: Divide the grid into some pentomino shapes along the gird lines. The shapes may be used more than once, with rotations and reflections allowed. Identical shapes may not touch each other through the edges. Given letters must be contained in the shape that they represent. Then draw a loop that moves horizontally or vertically between cell centres, and enters and exits every Pentomino exactly once. Shaded cells, if any, cannot be used by the loop. Given numbers indicate that the loop uses that many cells of the Pentomino containing the number. 

Puzzlerium Tour: Snakeout

The Puzzlerium channel does not have followers yet. These puzzles and videos are of good quality. So, do subscribe. I do everything myself - from construction to testing to shooting and editing. 

 

Rules: Place a snake whose path is 1-cell wide. The snake does not touch itself, not even diagonally. In the end, no two white cells in the same row or column can contain the same number. Two orthogonally adjacent cells with the same number cannot both be used by the snake.

About Snakeout: Snakeout is due to Anurag Sahay. It was first published in 2019.

Puzzlerium Tour: Rekuto

Rekuto is one of those puzzles that have remained low among other more popular ones. Nevertheless, I thought it was worth including in the tour and so I wrote one. This puzzle will also attract a solving video. 

  

Rules: Divide the grid into rectangles such that each rectangle contains exactly one given number that represents the sum of the width and length of the rectangle. Each cell in the grid must be part of a rectangle.

About Rekuto: Another Nikoli style, this region division puzzle has remained under the shadow of its cousin Shikaku, so much so that more information seems elusive.

Puzzlerium Tour: Interstellar

Rules: Draw a closed loop whose path does not branch out or intersect itself, and passes through the centres of some of the cells horizontally or vertically. The loop must enter and exit some of  the outlined regions exactly once, pass through all of the cells in every such region, and leave the entirety of the rest of the regions. Then, place one star in each of the regions that the loop does not pass through. Stars cannot touch each other, not even diagonally. None of the rows or columns may contain more than one star each.

About Interstellar: Invented by Anurag Sahay, Interstellar debuts with the puzzle published in this post.

Puzzlerium Tour: Ripple Loop

 

Rules: Draw a closed loop that connects the centres of all cells horizontally or vertically. When two circles are edge-adjacent, the loop must go straight through one, and make a right angle turn in the other.

About Ripple Loop: Invented by Anurag Sahay, Ripple loop was first published in 2017.

Puzzlerium Tour: Statue Park (Tapa-like clues)

Today's offering from Puzzlerium is a Statue Park puzzle, albeit with a different presentation. It pains me that even to this day, puzzles involving Pentomino shapes don't really enjoy the same status as some Number placement puzzles do. Statue Park, a puzzle that deals with Pentomino shapes, has been on the scene for nearly a decade now. Although it doesn't really need to be tweaked further for what it is, here is my version of Statue Park when it crosses over with Tapa, in a loose sense of that. 

Note that while Statue Park asks us to use ALL of the shapes given, I rather thought this variant was more fun without that constraint. I believe I am the first to explore this variant, unless I am missing something.

So, here is what the rules look like: 

Rules: Shade in some cells such that all of the shaded cells form some (or all) of the given shapes, without repetition, and with rotation and reflection allowed. Shapes cannot be orthogonally adjacent to each other. In the end, all unshaded cells must be connected in a single group through other unshaded cells. Numbers in a cell indicate how many Pentomino cells are contained in a continuous shaded cell block in its surrounding cells. If there is more than one number in the clue cell, there has to be at least one white cell separating the black cell blocks

About Statue Park: Statue Park was invented by Palmer Mebane and was first published in 2011.

Puzzlerium Tour: Heterocut

 Solution walkthrough for the Nurikabe is now online:

Rules: Divide the grid into some regions. No two regions can have the same shape; rotations and reflections are considered the same shape. Some borders are already given. Arrows on these borders (where given) always point to the larger of the two regions. All region sizes are in the given range.

About Heterocut: Heterocut was invented by Anurag Sahay, and was first published in 2008.

Walkthrough video for today's Heterocut puzzle is linked here:

 

Puzzlerium Tour: Nurikabe

Solution walkthrough for the Shikaku Fillomino is now online:

https://youtu.be/v3DYPfqWy38

Rules: Shade some cells so that all shaded cells are connected and no 2×2 square is completely shaded. Cells with numbers cannot be shaded. Each group of connected unshaded cells forms an island; islands can touch each other diagonally. Each island must contain exactly one number that is equal to the size of that island.

About Nurikabe: This genre was invented by Nikoli Puzzles. Nurikabe was first published by Nikoli in 1991.

Enjoy this Nurikabe and expect a video walkthrough along with the next puzzle soon.

 

Puzzlerium Tour: Shikaku Fillomino

Today's offering from the Puzzlerium is a couple of back-to-back puzzles. First up is a hybrid between Shikaku and Fillomino. Fillomino is a favorite region division puzzle. Ever since I was enticed by this genre, I have written dozens of fillomino puzzles and I can't  get enough of it. Shikaku is one puzzle that most of us don't find very interesting in the classic form, while it's mutations and hybrids can change that in many ways.

I wanted to make the most of what Geometry can do in a Shikaku Fillomino and the puzzle I am presenting here seems to have met my expectations.   

Rules: Divide the grid along the gridlines into some regions, and fill each of the empty cells with a number. When two cells containing the same number touch along an edge, they must belong to the same region. Given numbers represent the area of the region they belong to. A region may contain none, or one or more of the givens. All regions need to be rectangular (as in Shikaku).

Solution videos for the Slitherlink and Go Square puzzles are linked here:

https://youtu.be/xiGVkWNz2WU

https://youtu.be/QQo0pbd5W-4

Up next on the series is a delightful Nurikabe that should be available later today, and should I find time, walkthrough videos for both the Fillomino and Nurikabe should be out in the same post. 

Puzzlerium Tour: Go Square

Solution video for today's puzzle as well as for the Slitherlink should be out soon. Next on the series is a region division puzzle that is a hybrid between two Nikoli puzzles, which will then be followed by an engrossing Tapa.

Rules: Draw a single loop that has an orthogonal path and visits all cells exactly once each. Numbers indicate how many 2x2 squares in the corresponding outlined region have all of their four cells visited in immediate succession to each other. 

About Go Square: Go Square is due to Anurag Sahay, and debuts with the puzzle published in this post.