Puzzlerium Tour: Arithmetic Carvings

 

Rules: A wall is hidden in the grid. Each horizontal row contains bricks of 1 unit height and length 1 and longer, lodged one beside the other. Two bricks of the same length cannot share an edge. Each brick has either a single digit, or an arithmetic expression with two single-digit numbers from 1 to 9, written on it, one number per cell. One of four standard operators +, -, x, and /, is used in each operation. The length of the brick must be equal to the expression's result or the lone digit it contains. Expresions do not evaluate to negative or non-integral values. No two equal digits or operators can touch each other in any way. Operators are always placed between the operands.

About: This puzzle type was invented by Anurag Sahay.

Puzzlerium Tour: Circular Squares

  

Theme: Counting Down

Rules:  Place a few squares (rectangle with equal sides) of side 1 or larger so that they do not touch or orverlap each other except at a point. Each given number is part of a square of side equal to the number. A square can contain one or no given number. 'X'-marked cells, if given, cannot be used. It must be possible to draw a loop (not necessarily unique) that does not interset itself and moves horizontally or vertically between centers of cells and visits each placed square once in its entirety. The loop must visit exactly one empty cell during every changeover between two squares. 

About: This puzzle type was invented by Anurag Sahay.

Puzzlerium Tour: Double Block/Skyscrapers

  

Theme: One puzzle, two sets of rules

Rules: 

Double  Block: Blacken two cells in each row and column, then place numbers 1 to 3 in empty cells, such that each row and column contains numbers 1 to 3. Each clue represents the sum of numbers (including the "sum" of a single number) between shaded cells in the row or column the clue points at. 

Skyscrapers: 

Place one digit from 1 to N into each cell of the square grid where N is the length of the square's side, so that each number appears exactly once in each row and column. Each number inside the grid represents a skyscraper of its respective height. Outside clues indicate the number of skyscrapers visible in that direction, Smaller skyscrapers are hidden behind taller ones.

Puzzlerium Tour: The Hyperloop

Rules:  The grid is a layout of the Hyperloop network. Clue cells represent endpoints of each track, the length of the track represented by the given number. A track's path is a straight line between cell centers, and two tracks may only intersect inside a pod, and they always go straight through an intersection. Pods are 2x2 squares that do not touch each other, not even at a corner. No cell inside a pod can contain a 90 deg. turn of the path of the track. Not all cells in a pod need to contain tracks, and not all ccells need be intersections. Also, the stations can be a part of the pods. Given numbers outside the grid indicate how many pods are located in the corresponding direction. Although hypothetical, two adjacent cells can be endpoints of the same track.

About: This puzzle type was invented by Anurag Sahay.

Puzzlerium Tour: Fillomino

  

Theme: Odd vs Even

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.

Puzzlerium Tour: Tetrahexanatomy

 

Rules: Place some of the Tetrahexes, twice each. All of the clue cells belong to the shapes. 'X'-marked cells, if any, cannot be used.  Tetrahexes may be rotated and reflected but cannot touch each other. Each given line's path alternates between dead-end cells and the other cells.

About: This puzzle type was invented by Anurag Sahay.

Puzzlerium Tour: Squares and Rectangles

    

Rules:  Divide the grid into rectangles and squares that do not overlap. Areas of the same size (in number of cells) cannot share an edge. Each given black circle must be inside a square and each given white circle must be inside a rectangle. No given circles can be on edges or corners of rectangles or squares. Each given circle represents exactly one figure. Each figure has to contain one given circle. 

About: This puzzle type was invented by Anurag Sahay.

Puzzlerium Tour: Close Quarters

   

Rules:  Place a few squares of side 1 or larger so that every cell in the grid belongs to one or more squares. Squares of the same side length cannot have their sides overlap, but can overlap partially with one another (share cells). Conversely, Squares of different side lengths can have their sides overlap, but cannot share cells. Given numbers are part of a square of side equal to the number. A square can contain one or no given number but not more than one given. 

About: This puzzle type was invented by Anurag Sahay.

Sixth Puzzlerium Optimization Championship

The championship concluded a week ago. Vladimir Burik takes the first place again. Sergei Podshivalov finished second. Thanks and congratulations to all of the entrants. Standings table is now available. Pentomino packing was the most voted puzzle.

150

3, 72

9

43, 86

1470

Puzzlerium Tour: Conveyer Belts

Rules:  Subdivide the grid into pairs of regions such that each pair encloses exactly one given circle. The circle should correspond to a border between the two regions  Within each such pair of regions, it must be possible to draw a loop (not necessarily unique) that does not intersect itself and moves horizontally or vertically between centers of cells and traverses the entirety of the pair. Regions within a pair may or not be identical with each other, but must be equal in area. Also, no two identical regions from across different pairs may share an edge. 

About: This puzzle type was invented by Anurag Sahay.

Puzzlerium Tour: Pivotal Sequences

 

Rules:  Enter numbers 1 to N inside each outlined region where N equals the number of cells in the corresponding region. No two equal numbers can share an edge. Some numbers are already given. When a number 'A' is greater than all other numbers in its region, the following should hold true: 

If an adjacent number 'B' from another region is greater, it should be possible to find a sequence that starts in the cell containing 'B', and moves horizontally or vertically through cell centers within the region, and encounters numbers in descending order until the length of the path (number of cells used) is equal to or greater than 'A'. Multiple sequences can overlap and sequences could be subsequences of larger ones. It is possible that a puzzle has no such sequences at all.

About: This puzzle type was invented by Anurag Sahay.

Puzzlerium Tour: Tapa (Indispensable)

  

Theme: Clue Symmetry

Rules: Paint some squares to create a continuous wall of connected cells. Number(s) in a cell indicate 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. Clue Cells cannot be painted. 

Additionally, the grid is subdivided into bold outlined regions. If a region has a given number in the top left corner of a cell, the given number indicates how many of the shaded cells in that region are not orthogonally or diagonally adjacent with any of  the clue cells (including clue cells that lie outside the region).

About: This variation on Tapa was invented by Anurag Sahay.

Puzzlerium Tour: Statue Park (Three Halves)

 

Penpa+

Rules: Shade in some cells such that shaded cells form each of the Pentomino shapes without repetition. You can rotate and reflect the shapes, but they cannot be edge-adjacent to one another. Black circles represent spaces contained in a shape, whilst white circles represent spaces that may not be contained in a shape. In the end, all unpainted cells must be connected in a single group through other unpainted cells (including those containing white circles). Each bold outlined region must include a full pentomino and a half of another pentomino - half meaning either 2 or 3 cells while the other 3 or 2 cells contained in an adjoining region.  

About: This variant of Statue Park was invented by Anurag Sahay.

Puzzlerium Tour: Snake (Sensors)

  

Rules: Place a snake - a path of shaded cells that does not touch itself, not even diagonally. Both end points of the snake are given as marked with 'S'. Cells marked with 'x' are either part of the snake or not. In the latter case, the snake cannot make a turn in any of the upto eight cells adjoining the clue cell.

About: This variant of the Snake puzzle was invented by Anurag Sahay

Puzzlerium Tour: Linear Automaton

 

Theme: Two Diamonds

Rules: Draw a single, non-intersecting loop, vertically or horizontally through the grid lines. A black circle has the loop turn in both the adjoining nodes, while a white circle has the loop turn in exactly one of the adjoining nodes and go straight through the other node.

About: Linear Automaton was invented by Anurag Sahay

Puzzlerium Tour: Tapa (Affinity)

 

Theme: Symmetry

Rules: Paint some squares to create a continuous wall of connected cells. Number(s) in a cell indicate 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. Clue Cells cannot be painted. 

Additionally, there are bold outlined regions. If a region has a given number in the top left corner of a cell, there has to be at least one painted cell block that is adjacent to as many painted cell blocks from other regions as the given number.

About: This variation on Tapa was invented by Anurag Sahay.

Puzzlerium Tour: Circular Tetromino

 

Rules:  Place a few tetrominoes into the given grid. Tetrominoes can only touch each other diagonally. Given letters must overlap with the tetromino they represent. A tetromino may contain one or more or no givens. 'X'-marked cells, if given, cannot be used. It must be possible to draw a loop that does not interset itself and moves horizontally or vertically between centers of cells and visits each tetromino once. The loop must enter and exit every tetromino in its dead-end cells, and must visit exactly one empty cell during every changeover between two tetrominoes. 

About: This puzzle type was invented by Anurag Sahay.

Puzzlerium Tour: Tapa (Genome)

   

Theme: Repeated clues

Rules: Paint some squares to create a continuous wall of connected cells. Number(s) in a cell indicate 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. Clue Cells cannot be painted. 

Additionally, adjacent painted cell blocks from different regions cannot be of the same size.

About: This variation on Tapa was invented by Anurag Sahay.

Puzzlerium Tour: Masyu

  

Puzz.link

Rules: Draw a single loop that consists of horizontal and vertical paths through the centres of cells, and does not intersect itself or enter the same cell more than once, and has to pass through all of the circles. The loop must pass straight through the cells with white circles, making a turn in at least one of the cells immediately before or after visiting each white circle. The loop must make a turn in all the black circles, but must go straight in both cells immediately before and after visiting each black circle.

Puzzlerium Tour: Lost in the Woods

There is this WSPC 2022 guessmaking contest (aptly?) titled "Crystal Ball" running somewhere that I have entered because I can guess, and as the theory of probability suggests, I am as much likely to not win as anyone is. I figured most of those questions had options with equally probable outcomes. Win or not, I guess I am the first entrant.

Today's puzzle is again a new loop type.

Rules: Draw a single, non-intersecting loop, that follows vertical and horizontal paths, and visits each of the areas outlined in bold. Given clues are only relevant within the outlined area that contains them. The loop turns in one or more cells located in each of the given directions (within the area), while it does not turn in any of the directions not given.

About: This puzzle type was invented by Anurag Sahay.

Puzzlerium Tour: Pendulum

 

Rules: Draw a single, non-intersecting loop, that follows vertical and horizontal paths, and visits each of the areas outlined in bold. Every instance the loop enters an area, it either makes a turn or goes straight in both the cells that it visits immediately after entering and before leaving the area (when just one cell is visited between entry and exit, the rule is satisfied automatically). Given circles indicate the areas on either side of the circle are passed successively at least once.  

About: This puzzle type was invented by Anurag Sahay.

Puzzlerium Tour: Anymino (Double)

   

Rules: Shade in some cells such that shaded cells in each outlined area form two polyminoes that may only touch each other at a point. No 2×2 square can be shaded completely. All shapes must be connected to form a single contiguous group of shaded cells. Identical figures, regardless of rotation or reflection, cannot share an edge. Each shape must be adjacent with one or more shapes of the same size as it's.

About: Anymino was invented by Anurag Sahay.

Puzzlerium Tour: Nanro

 

Puzz.link

Rules: Insert a number into some of the cells so that each outlined area contains at least one number which represents the number of cells containing a number in that area. Where two numbers connect across a region boundary, those numbers must be different. All numbers must form one, connected area with no 2x2 areas of numbered cells. Some numbers may already be given.

Puzzlerium Tour: Limbs

 

Rules: Given hexagonal grid contains some bold outlined areas. Draw a two-limbed figure (a line that turns in one cell and is three or more cells long) inside each of the areas. Two figures with the same angle of turn cannot touch. Given numbers indicate the length of the figure (the number of hexagons occupied). Circles, if given, indicate the cell where the figures have a corner.

Puzzlerium Tour: Shape It Up

Rules:  Place the complete set of tetrominoes, seven, including unique reflections, into the given grid. Tetrominoes cannot touch each other, not even diagonally. Each tetromino must be divided equally in two regions. Also, a tetromino cannot be the same as either of the regions it is placed in. 'X'-marked cells cannot be used.

Puzzlerium Tour: The Expressway

Rules: Draw a single, non-intersecting loop, that follows vertical and horizontal paths, and visits each of the areas outlined in bold. Within every area, the loop visits all cells of one color and leaves all of the other.  

About: This puzzle type was invented by Anurag Sahay.

Puzzlerium Tour: Competitive Loop

  

Rules: Draw a single, non-intersecting loop, that has vertical and horizontal paths, and visits all of the given circles. If a cell orthogonally adjoining with a circle is visited, the loop must turn/go straight in that cell too (if it turns/ goes straight in the circle).  

About: This puzzle type was invented by Anurag Sahay.

Puzzlerium Tour: Accord

Rules: Shade in two or more cells in each outlined area such that all of the shaded cells in each outlined area are edge-connected. All shapes must be connected diagonally. Shaded cell groups of the same size cannot touch across regions in any way, not even diagonally. Shaded cell groups of different sizes may only touch each other diagonally.

About: This puzzle type was invented by Anurag Sahay.

Puzzlerium Tour: Skyscrapers (Crowded)

  

Rules: Place one or two digits from 1 to N+1 into each cell of the square grid,  where N is the length of the square's side, so that each number appears exactly once in each row and column. One cell in each row and column must contain two digits. Each number inside the grid represents a skyscraper of its respective height. The outside clues indicate the number of skyscrapers visible in that direction, Smaller skyscrapers are hidden behind taller ones. Cells containing double digit numbers house two skyscrapers - the taller skyscraper always behind the shorter one (from all applicable viewing standpoints).

About: This variant was invented by Anurag Sahay.

Puzzlerium Tour: Air Show

 

Rules: Draw a single, non-intersecting loop, that has vertical, diagonal and horizontal paths, and visits all of the given circles. The path of the loop makes a 90-degree turn in each black  circle - may also enter and leave diagonally - and a turn of any other angle in white circles. The path cannot go straight through any circle. The circles are visited in an orderly manner - all black circles are visited successively and so are the white circles. Grey circles are either black or white, their color needs to be determined. 

About: This puzzle was invented by Anurag Sahay.