Theme: Ho-Ho.. It's a puzzle
Rules: Draw a single, non-intersecting loop, vertically or horizontally through the centres of the cells. The loop visits each outlined region at least once and passes straight through exactly as many cells in each region as many times it visits that region. Given numbers, if any, indicate that number.
About: “The Highway” was invented by Anurag Sahay.
Rules: Draw two straight lines in each outlined region without any bends - one entirely inside and the other running into a neighbouring region without crossing any other region in between. There will be one line of the second kind for each pair of regions. Given numbers indicate the lengths of the internal lines. Dots, if given, mark an end point of one of the lines. In the end, all unused cells are required to be connected through their edges. Lines of the same length cannot touch each other orthogonally. Lines do not cross or overlap one another.
About: "Spies and Civilians" was invented by Anurag Sahay.
Rules: Divide the grid into pentominoes such that every cell in the grid is a part of exactly one pentomino. Pentominoes of the same shape (rotations and reflections of a pentomino count as the same shape) cannot touch each other along an edge, but they may touch diagonally. Inside each pentomino, draw horizontal or vertical lines that connect each of its cells through their centers. Lines belonging to one pentomino do not extend to other pentominoes. Each 'A' indicates that the cell containing it has at least one right angle made by the lines. All such 'A's are given.
Rules: Shade in some cells such that no 2x2 square is shaded completely. All shaded cells form a connected group. Given black numbers indicate the number of dead-end cells of the coral inside the corresponding region, while green givens indicate the number of other shaded cells.
About: Binary Coral was invented by Anurag Sahay.
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Rules: Draw a single, non-intersecting loop, vertically or horizontally through the centres of the cells. The loop visits each outlined region at least once, and makes a total of exactly as many turns in each region as the number of its visits to that region. Given numbers, if any, indicate that number.
About: The Pass was invented by Anurag Sahay.
Rules: Draw a single, non-intersecting loop, vertically or horizontally through all cells. Clues to the left/top of the grid indicate the number of horizontal/vertical straight line segments in the correspoding row or column longer than both of their adjoining segments (two segments are adjoining if they both turn at the same point). Clues to the right/bottom of the grid indicate the number of horizontal/vertical straight line segments in the correspoding row or column shorter than both of their adjoining segments.
About: Meta Loop was invented by Anurag Sahay.
Theme: '21
Rules: Subdivide the grid into two areas of connected cells that solve as separate puzzles. The division can only be done along the given bold outlines - no outlined region belongs to more than one puzzle. Given shaded cell does not belong to the grid and is not used by either puzzle. Rules of individual puzzles follow:
Oscillatory: Draw a single non-intersecting loop vertically or horizontally through some cells. The loop must visit each bold outlined region once. In every second region visited along the path of the loop, the loop uses all the cells. And in every other region, it leaves one or more cells empty.
LITS: Shade in some cells such that each outlined area contains exactly four shaded cells that form a tetromino. 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 and reflection, cannot share an edge.
Theme: Back to 2020
Rules: Place the given standard 10-ship fleet. Ships cannot touch each other, not even diagonally, but you may rotate the ships. Each given number indicates the length of the first ship visible in that direction. Every bold outlined region contains one ship. Some regions are colored to accentuate the theme.
Rules: The grid is a Primate Park divided into one or more cages. Each cage is made of partitions of the same size and each cage has the same number of partitions. Within each cage, partitions of identical shapes cannot share an edge. All partitions of the same size make a single cage - there cannot be two different cages with the same partition size. It must be possible for each caged animal to trace a path - not necessarily unique - through the entirety of its cage, and the path has to be a loop that does not intersect itself. Shaded cells are not part of any cage. All unshaded cells belong to cages. Partitions in different cages can be of any sizes as long as they are consecutive integers. Some partition outlines are given. Find all the cages along with their partitions.
About: Primate Park was invented by Anurag Sahay.
Shading in two of the quadrants (and words outside) are thematic and are not intended to have a consequence on the solve.
Theme: The persisting need for Social Distancing
Rules: Divide the grid into pentominoes such that every cell in the grid is part of exactly one pentomino. Pentominoes of the same shape (rotations and reflections of a pentomino count as the same shape) cannot touch each other along an edge (but they may touch diagonally). Given letters, if any, must be part of a pentomino with that letter’s shape. It is permissible for a pentomino to contain more than one letter.
Rules: Shade in two cells in each row and column. Place a white circle or a black circle in each of the unshaded cells. Adjacent cells sharing a side cannot contain circles of the same color. In the end, the grid must contain equal number of circles of either color, and each row and column must contain at least one circle of either color. Cells marked 'X' cannot be shaded or used by the circles. Numbers outside indicate how many circles of the given color are present between shaded cells in the corresponding row or column.
About: Tic Tac Bloc was invented by Anurag Sahay.
Rules: Fill in the gird with numbers 1 to 6, one per cell. No two cells adjacent by the side can contain the same number. Every row and column has its own combination: exactly 3 numbers, with each number from the triplet occurring at least once in that row. Multiple rows and columns are allowed to use the same combination.
About: Interlaced Files was invented by Anurag Sahay.
Rules: Draw a single non-intersecting loop vertically or horizontally through some cells. The loop must visit each bold outlined region once. In every second region visited along the path of the loop, the loop uses an even number of cells, while in every other region, it uses an odd number of cells. Letters 'O' and 'E', if given, indicate that the loop uses an odd/even number of cells in that region.
About: Euler's Expedition was invented by Anurag Sahay in 2021.
Rules: Locate two loops that do not overlap or cross with each other and that each follow Masyu rules, except, all circles in one of the loops would be inverted (a black functions as a white and vice versa).
Masyu: 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.
As one of the most passionate consumers of puzzles, I opine this has to be the most fun of Masyu variants.
Theme: As many dots as black circles
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. 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.
Some nodes are labelled with a black dot indicating a checkerboard pattern - the loop turns in one pair of diagonally opposite cells and goes straight through the other. Not all such nodes are necessarily labelled - meaning there possibly are unlabelled nodes following the same pattern.
Rules: Shade in two cells in each row and column and draw a single non-intersecting loop vertically or horizontally through some of the unshaded cells. Numbers outside indicate the total length of loop segments between the shaded cells in the corresponding direction.
About: Asteroid was invented by Anurag Sahay in 2021.
Rules: Draw a single non-intersecting loop vertically or horizontally through some cells. The loop must visit each bold outlined region once. In every second region visited along the path of the loop, the loop uses all the cells. And in every other region, it leaves one or more cells empty.
About: Oscillatory was invented by Anurag Sahay in 2021.
Edit: For those who solved this before I fixed the puzzle (there was an alternative solution). One cell in the 4-cell area on the top-right goes to the L-shaped area right below it in the fixed version.
Theme: Some Intel
Rules: Shade in some cells so that each bold outlined region consists of two adjacent shaded cells that form a domino - a domino cannot be adjacent to another, except diagonally. Then, draw a single non-intersecting loop vertically or horizontally through some cells. The loop must visit each bold outlined region once, including each domino in its entirety.
About: Domino Trek was invented by Anurag Sahay in 2021 and the puzzle here is the first to be put out.
Rules: Fill in the square grid of side N, with digits 1 to N, one digit per cell, so that each digit appears exactly once in each row and column. The clue in each outlined cage indicates the result of a mathematical operation applied successively to each of the digits in the cage, starting from the largest to the smallest for division and subtraction. The operation may or may not be given in the cage, but at least one of the four operations must apply. Digits can repeat within a cage.
An unfortunate event erased one digit off of each clue. Information about which place the digit was in is not given, but the digits that are still standing remain in the same relative positions. For example, a '24' cannot be restored to 420 or 204. So, all the given numbers as seen are remnants of multi-digit numbers. Restore each clue and solve the resulting TomTom puzzle.
About: This variant was invented by Anurag Sahay in 2021 and debuts today.
Rules: Draw a single non-intersecting loop vertically or horizontally through some cells. The loop must visit each bold outlined region once. In every cell visited in a region, the loop behaves consistently - either makes a turn or passes straight through. Between every two regions visited immeidate succession, the loop must either turn or go straight.
About: Two Worlds was invented by Anurag Sahay in 2021 and debuts today.
This post introduces a Pentomino variant.
Theme: The Dial
Rules: Place the full set of twelve pentomino shapes in the given grid without repetition. Pentominoes may be rotated and reflected, but may not touch each other, not even diagonally. Given black circles represent dead-end cells of the shapes, while the given white circles represent the other kind of cells belonging to the shapes. Not all circles are given.
About: Binary Pentomino was invented by Anurag Sahay in 2021.
Rules: Draw a single non-intersecting loop vertically or horizontally through some cells. The loop must visit each bold outlined region once. The number of cells visited in each subsequent region along the path of the loop must alternate between X and Y (X and Y are constants that generally are to be determined).
Theme: The Big and the Small
About: XY Loop was invented by Anurag Sahay in 2021 and debuts today.
Statistics say this is the 500th post. What better way to mark it than this delectable construction?
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 given number, and that number indicates the size of the island. Each island also pairs up with one other island - the islands within a pair are connected through a corner. Such connections are exclusive - islands from any of the pairs never touch a third island outside the pair.
About: Binary Island Systems was invented by Anurag Sahay in 2021 and debuts today.
Rules: Draw a single non-intersecting loop vertically or horizontally through some of the cells. Some edges are marked either bold or dotted - with each category following either of two sets of rules - one set requiring the loop to use exactly one of the two cells on either side of the edge, and the other set either requiring the loop to use both cells or neither. The edge-ruleset mapping is not given and has to be determined.
About: Binary Loop was invented by Anurag Sahay in 2021.
Rules: Fill in the square grid of side N, with digits 1 to N+1, so that each digit appears exactly once in each row and column. One cell in each row and column contains two digits, while all other cells contain one digit each. The clue in each outlined cage indicates the result of a mathematical operation applied successively to each of the digits (and a two-digit number formed by joining two digits in a cell, if any) in the cage, starting from the largest to the smallest for division and subtraction. The operation may or may not be given in the cage, but at least one of the four operations must apply. Digits can repeat within a cage.
About : This variant of TomTom was invented by Anurag Sahay.
Vladimir Burik has reclaimed the Puzzlerium Optimization Championship as he registered a third win. Coming off a setback in the last edition, the Ukrainian came very close to a clean sweep, losing out on just one puzzle as the last edition's champion Gerhard Richter produced what is possibly the optimal construction of the "Pentomino Fortress". Vladimir impressed with a 39-pointer (is this optimal?) construction of the "Interior illumination" puzzle.
Detailed results can be found in this spreadsheet. Best solutions follow. A better construction is possible on "Six ways" (326 points, displayed at the end of the post).
"Interior Illumination" and "Skyscrapers (Exclusive)" were found to be the most liked puzzles.
Rules: Place a number from 1 to N into each cell of the square grid so that each number appears exactly once in each row and column, where N is the length of the square's side. In this variant, the clues inside the cages are removed, and the new clues indicate the result of one of the four arithmetic operations (+,-,x,/) applied to the results of the operations inside the first two cages encountered when looking in the direction of the clue. Results are always integral. When an operator accompanies a given, it means that operator has to be applied.
About : This variant of TomTom was invented by Anurag Sahay.
Rules: Some circles of two or more colors are given (the puzzle above has circles of two colors). Draw a single non-intersecting loop vertically or horizontally through all cells. If two circles of different colors are visited successively(without any empty cell between them), the loop must turn both immediately after and immediately before visiting those circles.
About: Convoluted was invented by Anurag Sahay in 2021.
Rules: Fill in every outlined area with numbers 1 to N without repition, where N is the number of cells enclosed in the area. Arrows indicate all directions with the closest cell containing the number in the clue cell. Equal numbers cannot share an edge.
About: Myopic Numbers was invented by Anurag Sahay in 2018.
Rules: Some water moleules are hidden in the grid. Each molecule is a trimino with the letter 'O' in the center and two 'H's in the ends. Locate all the water molecules in without overlapping, such that.every trimino includes at least one given letter. Then, draw a single loop through all cells. No two adjacent cells along the path of the loop may contain the same letter.
About: Aqua Loop was conceived by Anurag Sahay in 2021.
The fourth instalment of the prestigious “Puzzlerium Optimization Championship” begins today. Anyone interested can put their skills to test in a competitive setup.
You may download the PDF containing the puzzles and start solving. All instructions are detailed in the document.
Questions may be asked by commenting here or at the FB event
Theme: The odd "L" and the missing "L"
Rules: Divide the grid into pentominoes such that every unshaded cell in the grid is part of exactly one pentomino (Shaded cells remain unused). Pentominoes of the same shape (rotations and reflections of a pentomino count as the same shape) cannot touch each other along an edge (but they may touch diagonally). Given letters, if any, must be part of a pentomino with that letter’s shape. It is permissible for a pentomino to contain more than one letter.
Theme: Clueless
Rules: Divide the grid into pentominoes such that every unshaded cell in the grid is part of exactly one pentomino (Shaded cells remain unused). Pentominoes of the same shape (rotations and reflections of a pentomino count as the same shape) cannot touch each other along an edge (but they may touch diagonally). Given letters, if any, must be part of a pentomino with that letter’s shape. It is permissible for a pentomino to contain more than one letter.
Rules: Shade in exactly three cells in each of the bold outlined regions so that all of the unshaded cells are connected orthogonally in a single group. Shaded cells may only be diagonally adjacent. Every triplet of shaded cells within each region must be located identically with respect to each other. Clues outside give the number of shaded cells in the corresponding direction.
About: Complex Replicas was invented by Anurag Sahay in September 2021.
Theme: Just Fits
Rules: Shade in exactly two cells in each of the bold outlined regions so that all of the unshaded cells are connected orthogonally in a single group. Shaded cells may only be diagonally adjacent. No two pairs of shaded cells within each region may be located identically with respect to each other. Clues outside give the number of shaded cells in the corresponding direction.
About: No Replicas was invented by Anurag Sahay in September 2021.
Rules: Shade in exactly two cells in each of the bold outlined regions so that all of the unshaded cells are connected orthogonally in a single group. Shaded cells may only be diagonally adjacent. Every pair of shaded cells within each region must be located identically with respect to each other.
About: Replicas was invented by Anurag Sahay in September 2021.
Rules: Place a number from 1 to N into each cell of the square grid so that each number appears exactly once in each row and column, where N is the length of the square's side. Each number inside the grid represents a skyscraper of its respective height. The outside clues indicate either of two quantities - the number of skyscrapers of odd heights visible in that direction, or the number of skyscrapers of even heights visible in that direction. Smaller skyscrapers are hidden behind taller ones. Clues are unlabeled - which skyscrapers they represent has to be determined as the puzzle is solved.
The Puzzlerium Optimization Championship returns with the fourth edition on the 25th of September. The Facebook page will be updated with the event soon.
Rules: Divide the grid along the gridlines into rectangles such that every rectangle contains two circles and no circle is at the corner (every rectangle 1xn has 2 corners and mxn has 4 corners). No two rectangles of the same area (for example, 5x6 and 3x10) may be orthogonally adjacent.
About: Spotlight was invented by Anurag Sahay in September 2021.