# Questions tagged [grid-deduction]

Puzzles such as Sudoku or Kakuro, where the final state of a pre-existing grid must be deduced logically through clues placed within and/or around the grid. Use with the [logical-deduction] tag. For puzzles where you are given a list of clues which can be used to compose a grid to solve them logically, use the [logic-grid] tag instead.

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### 🐍 In the Loop 🐍

Follow the ouroboros down valleys and over mountains. Is it even going anywhere? EDIT (7 days after initial posting): The grid and Penpa+ link have been updated to an easier version, with more numbers ...
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### Help with Star Battle puzzle

I made it through all the easy levels without ever having to consciously divide the whole grid into specific regions. I've seen that this is a common technique, but it confuses me even more when ...
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### A Crabby Sudoku

I present a *deep breath* Even-Odd TetroThermoDoku. From the back of the name to the front: Rules Sudoku: Fill each cell with a digit 1-9 such that no number repeats in any row, column, or 3x3 heavy-...
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### Plumbing Issues

This is part 59 of the puzzle series Around the World in Many Days. Each part is solvable on its own. Dear Puzzling, This is a Pipes puzzle (also known as Net, FreeNet and NetWalk). Rotate some cells ...
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### A small board-puzzle

Place pieces (red) on the board, so every piece is adjacent to 4, 5 or 6 other pieces. I've created this puzzle myself playing around with cellular automatons.
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### Masyu: Four Colours

Draw four separate loops in the grid, one blue, one green, one grey and one red. Loops connect centres of cells horizontally and vertically and cannot cross over themselves or share any cell with each ...
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### Continue in 6x6 Towers puzzle

How can I continue with this Towers puzzle?
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### Cover me, I'm going in!

This is part 58 of the puzzle series Around the World in Many Days. Each part is solvable on its own. Dear Puzzling, This is a diagramless checkerboard crossword. Empty cells are either blue or white;...
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### Riverboat Soufflé

This is part 57 of the puzzle series Around the World in Many Days. Each part is solvable on its own. Dear Puzzling, This is a bicolour Masyu puzzle. Draw two separate loops in the grid, one red and ...
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1 vote
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So I have been using a site called Brain Bashers, which is a site filled with logical deduction puzzles, because I like trying to master different logical deduction puzzle types. I have finished the ...
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### a few signposts

Assign an integer (1 through 16) to each cell so that: 16 is in the cell with the star; and each integer's arrow points to its successor (i.e. the next integer), though not necessarily in the ...
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### Product = Sum Sudoku (Royal Statistical Society Christmas Quiz 2023)

Normal Sudoku rules for this grid size apply. The product of the numbers on each pink diagonal equals the sum of the numbers in the blue square. This puzzle is from the now closed contest at: https:/...
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### Continue with sudoku - how do I scan for next steps?

I filled some cells, but am stuck here. I cannot go any further. How do I advance? How would I scan the Sudoku to recognize next steps? I've taken the puzzle from https://play.google.com/store/apps/...
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### A hard(?) 15-X puzzle

Below is the puzzle I came up with before writing Create a 15-X puzzle with a unique solution. Rules of the puzzle: A 6x6 grid is given. Fifteen cells are marked with an X. Use polystrips of lengths ...
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### Create a 15-X puzzle with a unique solution

Background Last week, Brandan came up with a grid-deduction genre about filling a 6x6 grid with polystrips of lengths 1 through 8, using each length exactly once. A polystrip cannot bend twice in a ...
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### Minimally clued 4x5 Hidato (4 clues)

Puzzle attribution: Me :) Background So as you might or might not know, I have been studying the minimum number of clues needed to force a unique solution in Hidato for variously sized boards. I ...
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### 5x5 Hidato with 4 single-digit clues

Goal of Hidato: Fill in a grid with a series of consecutive numbers that connect each other horizontally, vertically, or diagonally. Yesterday I posted New record for minimally clued 5x5 Hidato, ...
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### How do I constrain a puzzle and keep a singular solution?

I am tinkering with a puzzle framework that has the following rules: In a 6x6 grid of squares, arrange 8 strips of connected squares such that there exists exactly one strip of every length (i.e. a ...
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### New record for minimally clued 5x5 Hidato

CrSb0001 has been studying the minimum number of clues to force a unique solution in Hidato for variously sized boards. They came up with a 5x5 Hidato with 5 clues but it was found that it has ...
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### Minimally clued 5x5 Hidato

Puzzle attribution: Me Goal of Hidato: Fill in a grid with a series of consecutive numbers that connect each other orthogonally or diagonally To get the green checkmark $\color{green}✓$: Solve the ...
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### Binary Grid Challenge and X & O Conundrum

You are given a 5x5 grid with some cells filled with either "X" or "O". Your goal is to fill the remaining cells with "X" or "O" following these rules: Each row ...
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### What is the minimum amount of numbers needed to create a 4x4 Hidato with a unique solution?

Goal of Hidato: Fill in a grid with a series of consecutive numbers that connect each other horizontally, vertically, or diagonally. So I have been working on figuring out the minimum number of ...
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### Is the 7-clue 6x6 Sudoku solvable?

So I was trying to find an 8-clue 6x6 Sudoku because I knew from this paper that only 8 clues were needed to create a 6x6 Sudoku with a unique solution. However, I have managed to find one with 7 ...
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### Invalid Jigsaw Sudoku Layout

The Jigsaw Sudoku Layout below is invalid (no Latin Squares exist for it). Why? Please find a short, yet complete, explanation (no computations involved). ...
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### Light Up (Akari), but on a real projective plane!

This is a Light Up (aka Akari) puzzle, except it is on what is called a real projective plane. A real projective plane is, simply put, just a Möbius strip with a single edge except for the fact that ...
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### An unusually tricky Galaxy

Background I love Simon Tatham's Puzzles, especially for killing the odd few minutes. One of the available puzzles is Galaxies, based on Tentai Show. I can usually solve these in anywhere from 30 ...
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### An Irregular Colombian Sudoku

Solve the Irregular Sudoku below (by Xavier Castillo), where the usual rules apply. The dots outside the board on top indicate how many cells in the corresponding column or row of that board contain ...
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This is part 55 of the puzzle series Around the World in Many Days. Each part is solvable on its own. Dear Puzzling, This is a non-consecutive thermo sudoku. Fill the grid so that each row, column ...
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### What can I deduce next about this daily Light Up (Akari) puzzle? (Feb. 22, 2024, 7x7 Hard)

So yesterday, I was searching for online logical deduction puzzles when I came across this website called Brain Bashers which is a site filled with many different types of puzzles. I have been going ...
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### What can I next logically deduce in Day 62 of the Minesweeper Advent Calendar? (Fake 3D)

So I have gotten back into playing the Minesweeper Advent Calendars on heptaveegesimal.com, and recently came across the 2023 Minesweeper Advent Calendar. I am currently trying to beat Day 62, which I ...
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Think of classic Minesweeper game, with the following list of restrictions on the placement of mines: C (Connected): All mines are connected via 8-way neighborhood (orthogonal and diagonal). Q (Quad):...
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### The Minesweeper Puzzle That Might Stump People

I thought this might be a different kind of puzzle. This is a game of Minesweeper that I played earlier today. All standard rules apply. For those who don't know, the number inside of each cell ...
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The puzzle here is to analyze the following Slitherlink configuration and show that it is impossible. ...
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### Continue a hard Loopy/Slitherlink puzzle without brute-force

This is a classic Slitherlink puzzle from Simon Tatham's Portable Puzzle puzzle collection. I was stuck at the position shown for quite a while until I found a way to continue by logical deduction. I ...
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### Unchained Again

This is part 53 of the puzzle series Around the World in Many Days. Each part is solvable on its own. Dear Puzzling, The black and white circles in this grid form a Masyu puzzle. Draw one continues ...
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### A Colombian Jigsaw Sudoku

This is a Colombian Jigsaw Sudoku where the usual rules apply, but with irregular boxes. The dots in the right-hand scheme indicate how many of the numbers in a particular row or column are correctly ...
182 views

### How do I transcribe a Kakuro into a Google Sheets?

As other questions of mine mentioned, I have been slowly working through some PDF puzzle books. I will shortly come up on Kakuro puzzles. Here is an example from the Wikipedia article: The parts ...
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### 27 Directional Lights Celebrate 2024

Let us celebrate the start of 2024! (1 month late...) Direct each light (yellow) such that all unlit squares (white) are lit. Walls (black) block light from going through. Some clarifications of the ...
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### One more Colombian Sudoku

Here is one more Colombia Sudoku devised by Xavier Castillo. The usual sudoku rules apply. The dots outside the board above indicate how many cells in the corresponding column or row of that board ...
383 views

### Creeper Lighting

There are two sets of similar but separate puzzles here; the white puzzle (with white cells) and the black puzzle (with black cells). Each puzzle is solved independently. Each number is a "...
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### Hardcore Lighting - Excalidraw

Each yellow cell is a light that shines in exactly one direction, horizontally, vertically, or diagonally, endlessly, and goes through any block as long as the block is not a wall. Black cells do not ...
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### Nurikabe: Back to basics

Rules of Nurikabe: Shade some cells in the grid. Each area of unshaded cells must contain exactly one number, which indicates the size of that area. Two unshaded areas may not share an edge, but they ...
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### Minesweeper Queens

Based off of: Ken Duisenberg's Puzzle of the Week Oct. 15, 2003: Minesweeper Queens For the puzzle, in the given diagram, the numbered squares are empty, from which the given mines can be attacked by ...
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### Aquatic Giants – Heyawake / Marching Bands

This is part 52 of the puzzle series Around the World in Many Days. Each part is solvable on its own. “One, two, three, four, five, I love marine wildlife.” – unknown Dear Puzzling, The grid on the ...
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1 vote
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### What‘s the next step to solve this 10x10 nonogram?

I got stuck on this nonogram (picross) from the game “Murder by Numbers”: What is the next step from here?
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### On solving the minimally clued 8x8 Sudoku

So I have been doing research on the minimal amount of numbers needed to create an 8x8, and found this paper which went over the minimum amount of clues needed for a sudoku to have a unique solution ...
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### Orange on Turquoise

This is part 50 of the puzzle series Around the World in Many Days. Each part is solvable on its own. Dear Puzzling, This is a Beaches puzzle (or tricolour Aquariums, if you prefer). Shade some cells ...
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### sums and differences in consecutive grid [closed]

Fill in each square of the grid with a number from $1$ to $16$, using each number exactly once. Numbers at the left or top give the largest sum of two numbers in that row or column. Numbers at the ...