Shintaro Fushida-Hardy/Puzzles

Shintaro Fushida-Hardy

About: this is a collection of several pencil puzzles I have made (and am particularly happy with). Many more of my puzzles are available on my Logic Masters page. Pencil puzzles are a style of logic puzzle where the puzzle itself can be drawn with pencil on paper, and the solver is required to "fill the grid". (For example, puzzles you see in magazines and news papers.) At least ten of my puzzles have been featured/solved on Cracking the Cryptic.

Puzzles are given difficulty ratings from one to five stars. They are also listed in roughly increasing order of difficulty. (Most of my puzzles are fairly difficult, sorry about that.)

Puzzle images can be enlarged by clicking them.

Mystery Killer Primes ★☆☆☆☆

This is one of the first pencil puzzles I ever set.

Rules:

5x5 Latin square: every row and column contains the digits 1 to 5 exactly once each.
Prime cages: the digits in each cage sum to a distinct prime number. The digits in a cage may repeat, but the prime sums do not repeat.

Logic Masters page for more information, online solving links, etc.

Poseidon ★★☆☆☆

This was the first non-sudoku puzzle I made. (Since then, I have overwhelmingly set non-sudoku puzzles.)

Rules:

Yin-Yang: shade some cells so that all shaded cells are orthogonally connected, all unshaded cells are orthogonally connected, and no 2x2 region is entirely shaded or unshaded.
In addition, place a digit (from 1 to 9) in every cell with an arrow. This digit is the total number of shaded cells in the indicated direction (including the cell itself, if it is shaded). No two shaded cells can contain the same digit, and no two unshaded cells can contain the same digit. (However, the same digit may occur once shaded and once unshaded.)
Cells without arrows do not contain digits.

Logic Masters page for more information, online solving links, etc.

Thermohaline Circulation ★★★☆☆

This was set for a "weekly Scojo setting prompt". The prompt was to set a loop puzzle with at most 10 clues.

Rules:

Standard Sudoku rules apply.
Loop: shade some cells to form a 1-cell-wide orthogonally connected loop. The loop may not touch itself orthogonally, but can touch itself diagonally.
Non-loop cells form several orthogonally connected groups. Such a group of size N contains exactly the digits from 1 to N.
Thermo-sightline arrows: Each cell with an arrow (called an 'arrow cell') lies on the loop. The digit in an arrow cell is the number of visible loop cells in the indicated direction, where non-loop cells obstruct vision. (The arrow cell is not included in this count). Additionally, digits increase along loop cells seen by an arrow, starting with the digit in the arrow cell.

Logic Masters page for more information, online solving links, etc.

Habitat 67 ★★★★☆

This was set for a "weekly Scojo setting prompt". The prompt was to set a puzzle using the Dutch flatmates constraint.

Rules:

Fillomino: Subdivide the grid into orthogonally connected regions such that regions of the same size do not share a border, and fill every cell with the number equal to the size of its region. Each "?" represents a digit from 1 to 9 which must be deduced.
Dutch flatmates: every cell containing the number 5 either has a number-1 cell above it, or a number-9 cell below it (or both).
Mod-3 groups: all cells containing numbers which are equal modulo 3 form a single orthogonally connected group. This means every cell in the grid belongs to one of three orthogonally connected groups. (I recommend shading cells to keep track.)

Logic Masters page for more information, online solving links, etc.

Seer ★★★★☆

This was set for a "weekly Scojo setting prompt". The prompt was to set a puzzle using X-sum clues and nabner lines.

Rules:

Chaos construction: divide the grid into regions, each consisting of orthogonally connected cells, and fill each row, column, and region with the digits 1 to 9 once each.
Sightline X-sums: clues around the grid are the sum of the first X digits in the corresponding row or column, where X is the first seen digit. Further, X is the number of cells belonging to the same region seen by the clue, where region-boundaries block vision. Each letter (S, E and R) represents a different digit from 0 to 9, and two-letter clues are interpreted as two-digit numbers. A "?" clue can be any number (not necessarily a single digit).
Nabner: digits along gold lines belong to a set of pairwise non-consecutive digits.

Logic Masters page for more information, online solving links, etc.

Iterations ★★★★☆

This puzzle was inspired by wisty's Battleship Deconstruction. However, instead of using Battleship to build a Sudoku, I've used Pentopia to build a Yajilin.

Rules:

Each cell in the grid is exactly one of four cell types, as follows:
1. Pentopia clues (blue, given)
2. Pentominoes (to be determined)
3. Shaded cells (to be determined)
4. Loop cells (to be determined).
In other words, you will locate both pentominoes and shaded cells (which are distinct from each other), and draw a loop through all non-clue, non-pentomino, non-shaded cells.
Pentopia: place some of the given pentominoes in the grid so that no pentominoes touch, even diagonally. Each pentomino may be rotated or reflected, but must not repeat in the grid (where rotations and reflections are considered the same shape). The given clues (blue) indicate all the directions (up, down, left, and right) where the nearest pentominoes are located when looking from that cell. (To clarify, if a clue has multiple arrowheads, the distance to the closest pentomino cell must be the same in each direction, and pentominoes cannot overlap arrow clues.)
Yajilin: shade some non-clue and non-pentomino cells in the grid, and draw a loop that travels orthogonally through the centers of all remaining (non-clue, non-pentomino, non-shaded) cells. Shaded cells cannot share edges with each other (although they may be adjacent to clue cells or pentominoes). Some pentominoes contain arrows with numbers: these count the number of shaded cells in the indicated direction. Note that any numbered arrows in pentominoes will rotate or reflect together with its pentomino when placed in the grid.

Logic Masters page for more information, online solving links, etc.

Cygnus ★★★★☆

This puzzle was inspired by Agent's brilliant permaculture puzzles.

Rules:

Amalgam: The 20x20 outer grid contains two (overlapping) 12x12 inner grids which must be located by the solver. One is a kurodoko, the other is a (directionless) yajilin. Clues in the overlap are both kurodoko clues and yajilin clues. Clues which are in neither inner grid are ignored. An "x" clue in an inner grid is designated as "unshaded" but has no numerical meaning.
Kurodoko: shade some cells so that no shaded cells are orthogonally adjacent and all unshaded cells form a single orthogonally connected area. Clues cannot be shaded, and represent the total number of unshaded cells that can be seen vertically and horizontally including themselves. Shaded cells and kurodoko-grid boundaries obstruct vision.
Directionless yajilin: shade some cells so that no shaded cells are orthogonally adjacent and draw a loop through all unshaded non-clue cells. The loop travels vertically and horizontally through the centers of cells. Clues cannot be shaded, and represent the total number of shaded cells vertically and horizontally. Only yajilin-grid boundaries obstruct vision.

Logic Masters page for more information, online solving links, etc.

Flat Cosmos ★★★★★

This puzzle is a counterpart to another puzzle I set, Holographic Principle. That earlier puzzle was about geometry being forced by projections from the boundary, but in this puzzle the universe is a flat torus.

Rules:

Chaos Construction: divide the grid into regions, each consisting of orthogonally connected cells, and fill each row, column, and region with the digits 1 to 9 once each.
Sightline arrows: a cell with arrow(s) counts the number of cells seen in the indicated directions combined, including itself. Entering different regions obstructs this vision.
Toroidal grid: for the purposes of chaos construction regions and sightline arrows, consider rows 1/9 and columns 1/9 orthogonally adjacent to one another.

Logic Masters page for more information, online solving links, etc.

Rule of Thirds ★★★★★

This puzzle was made for round 3 of the Puzzle Agency Championship in 2025, in which we were tasked with setting a puzzle that involves partitioning the grid into three orthogonally connected groups. (I ended up being runner-up in the competition.)

Rules:

Divide the grid into three orthogonally connected regions. Clues in the puzzle are region border clues of three ambiguous types, determined by the region they belong to. The phrase 'region border' refers to both cell edges along the perimeter of the grid, and cell edges between distinct regions.
Region 1: Distance clues. (Myopia) Arrows point toward the region borders closest to the clue. If a cell is clued by an arrow, then all possible arrows are given for that cell.
Region 2: Length clues. (Loop 12) Arrow-tips touch the longest straight segments consisting of region borders that share an edge with the clue cell. If a cell is clued by an arrow, then all possible arrows are given for that cell.
Region 3: Counting clues. Arrows point in directions with the most region borders. If a cell is clued by an arrow, then all possible arrows are given for that cell.

Logic Masters page for more information, online solving links, etc.

Mictēcacihuātl ★★★★★

This puzzle is a counterpart to another puzzle I set, Mictlāntēcutli. That earlier puzzle was unsigned ("more familiar"), but in this puzzle everything is oriented/signed.

Rules:

Directed U-Bahn: draw a directed loop network through the centers of some (non-clue) cells, which may branch or turn, but may not have any dead ends. More precisely, every branch and cross in the grid is a sink or source (to be determined). All loop segments must be directed, connecting a source to a sink. A digit outside the grid indicates how many times the corresponding line shape (i.e. a cross, branch, straight line, or turn) appears in the corresponding row or column, irrespective of the line shape's rotation.
Castle-Wall Delta: clues inside the grid count the number of loop network steps made towards the clue cell minus the number of loop network steps made away from the clue cell in all indicated directions combined.

Logic Masters page for more information, online solving links, etc.

Anableps ★★★★★

This puzzle was set for round one of the Pencil Puzzle Madness tournament. (I went on to win the competition!)

Rules:

Standard myopia rules apply: draw a loop which travels along edges of the grid, and does not branch or cross itself. Arrows point toward the loop segments closest to the clue. If a clue has multiple arrowheads, the distance to the closest loop segment must be the same in each direction.
Aquarium variant: The numbers around the grid indicate the number of shaded (water) cells in that row/column. Water can only be inside of the myopia loop, and water must have a loop segment or another water cell below it. Water follows the laws of physics: i.e. each orthogonally connected body of water must have the same surface level everywhere (including in U-shaped areas).

Logic Masters page for more information, online solving links, etc.

Tetropolis ★★★★★

This puzzle was inspired by MaizeGator's Let it Go and mathpesto's Thirteen Ghosts.

Rules:

Tetrochain: place some tetrominoes (blocks of four shaded cells) in the grid. Tetrominoes may not share any edges, but they must form a single diagonally connected network. Additionally, two tetrominoes which touch at a corner must have different shapes (counting reflections and rotations as the same).
Skyscraper clues: in a given row or column, each contiguous sequence of shaded or unshaded cells is called a 'skyscraper'. The 'height' of a skyscraper is the number of cells it is composed of. Each number outside the grid is the number of skyscrapers that can be seen from the clue in the corresponding row or column, where a skyscraper can be seen if it is taller than all preceding skyscrapers. (For clarity, in rows, skyscrapers are horizontal.)

Logic Masters page for more information, online solving links, etc.

Sabal ★★★★★

This puzzle is dedicated to MaizeGator, who I have been lucky to call my closest puzzling collaborator since shortly after I first started setting. He was pivotal in my introduction to pencil puzzles beyond sudoku. In 2024 he set Bonsai, a ciphered yin-yang sudoku, as a gift for me. This puzzle is also a yin-yang sudoku in reference to his gift, but I've combined it with fillomino and a huge grid, both of which I know MaizeGator loves!

Huge thanks to Agent, Christounet and the_cogito for taking the time to test either this puzzle or earlier versions in their entirety and providing very helpful feedback.

Rules:

Fillomino: divide the large grid into regions. In every cell, enter the size of the region it belongs to. No two regions of the same size may share an edge.
Yin-Yang Sudoku: normal Sudoku rules apply in the small grid. Additionally, shade some cells so that all shaded cells are orthogonally connected, all unshaded cells are orthogonally connected, and no 2x2 is entirely shaded or unshaded. Digits in arrow-cells count the total number of shaded cells in the indicated direction. (Shaded arrow-cells do not count themselves.)
Interactions: every cell in the Sudoku grid corresponds to a 3x3 box in the Fillomino grid. Consider the digit 'N' in some Sudoku cell.
- If 'N' is shaded, exactly N Fillomino regions visit the corresponding 3x3 box.
- If 'N' is unshaded, the number N occurs more frequently than any other number among the nine cells of the corresponding 3x3 box.
- To clarify, there is no negative constraint: both interactions above may hold true for any sudoku cell.
The dots in either grid have no rule implications, they are a visual guide to make scanning easier.

Logic Masters page for more information, online solving links, etc.