Questions tagged [logical-deduction]

A puzzle that requires formal logical deduction to arrive at the solution. This suggests more than merely reasoning through clues to find an answer (you might want [situation] for that).

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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 ...
gemmabomma's user avatar
12 votes
2 answers
303 views

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-...
bobble's user avatar
  • 10.4k
13 votes
1 answer
547 views

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 ...
Jafe's user avatar
  • 77.8k
17 votes
2 answers
1k views

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.
Dromlius's user avatar
  • 175
20 votes
2 answers
890 views

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 ...
Jafe's user avatar
  • 77.8k
3 votes
1 answer
409 views

Continue in 6x6 Towers puzzle

How can I continue with this Towers puzzle?
Alex Eh's user avatar
  • 31
-4 votes
1 answer
123 views

Logic and Geometry Problem #6

Is it possible for a deadlock to occur in Necklace? Can there be a square on which neither Red nor Blue can place a stone? If it is possible, I need to see an example of that. If a deadlock is not ...
Mark Steere's user avatar
10 votes
1 answer
1k views

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;...
Jafe's user avatar
  • 77.8k
1 vote
1 answer
159 views

What can I deduce about this daily Skyscrapers? (Mar. 18, 2024, 5x5 Easy)

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 ...
CrSb0001's user avatar
  • 2,241
25 votes
3 answers
2k views

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 ...
msh210's user avatar
  • 12.6k
6 votes
1 answer
231 views

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:/...
Will Octagon Gibson's user avatar
0 votes
0 answers
188 views

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/...
Abbas Baghirov's user avatar
6 votes
1 answer
165 views

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 ...
Bubbler's user avatar
  • 13.8k
13 votes
2 answers
217 views

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 ...
Bubbler's user avatar
  • 13.8k
17 votes
2 answers
2k views

Making a 2n-digit number divisible by 9

Alice and Bob play the following game, taking turns. Alice starts and writes a digit from the set M={1, 2, 3, 4, 5, 6} at the blackboard. Bob appends another digit from the set M until a 2n-digit ...
ThomasL's user avatar
  • 12.2k
13 votes
7 answers
2k views

Fewest number of prisoners needed

You are an assistant to the king, who has scheduled a party tomorrow. There are 1000 wine bottles in the king's possession, and unfortunately, 3 of them are poisonous. Consuming from any of these ...
Durgesh Patel's user avatar
3 votes
1 answer
208 views

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 ...
CrSb0001's user avatar
  • 2,241
6 votes
1 answer
176 views

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, ...
Bubbler's user avatar
  • 13.8k
11 votes
3 answers
601 views

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 ...
Bubbler's user avatar
  • 13.8k
4 votes
1 answer
212 views

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 ...
CrSb0001's user avatar
  • 2,241
13 votes
3 answers
1k views

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 ...
CrSb0001's user avatar
  • 2,241
5 votes
1 answer
466 views

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 ...
CrSb0001's user avatar
  • 2,241
20 votes
1 answer
830 views

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). ...
JCO's user avatar
  • 440
3 votes
1 answer
317 views

Place numbers 1 through 9 in boxes (☐☐×☐=☐☐+☐☐=☐☐)

So recently I was scrolling through Youtube when I came across this video from MindYourDecisions that was about solving a legendary math puzzle. The puzzle: Place the numbers 1 through 9 in the ...
CrSb0001's user avatar
  • 2,241
9 votes
1 answer
483 views

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 ...
CrSb0001's user avatar
  • 2,241
17 votes
2 answers
724 views

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 ...
Matthew's user avatar
  • 377
7 votes
1 answer
299 views

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 ...
Bernardo Recamán Santos's user avatar
19 votes
1 answer
1k views

Mercury in Centigrade

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 ...
Jafe's user avatar
  • 77.8k
2 votes
1 answer
150 views

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 ...
CrSb0001's user avatar
  • 2,241
2 votes
2 answers
173 views

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 ...
CrSb0001's user avatar
  • 2,241
34 votes
6 answers
6k views

The Devil's Shell Game

Inspired by the Skull Game in StoneStory RPG. You make a deal with the Devil. You are granted your deepest desire, in exchange, eventually, for your eternal soul. Every year, on your birthday, he ...
Hand-E-Food's user avatar
4 votes
2 answers
375 views

Lions vs. Pokémon

It is the year 10,000,000,000, and materalisation has been invented. At the same time, Nintendo has materialised every single Pokémon (countably infinitely many now!) to fight against finitely many ...
3-1-4-One-Five's user avatar
12 votes
1 answer
2k views

Add rules to Minesweeper until you can start with nothing

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):...
Bubbler's user avatar
  • 13.8k
5 votes
1 answer
202 views

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 ...
Truej's user avatar
  • 532
2 votes
0 answers
257 views

5 guards, and get rid of the timer!

I like the lies and statistics question, but it is a bit too violent, so I suggest a (slightly harder) and way less violent version. You are looking at the basement of your house, and you see three ...
3-1-4-One-Five's user avatar
7 votes
3 answers
1k views

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 ...
quarague's user avatar
  • 1,823
5 votes
1 answer
425 views

A Spelling Bee Champion And Some Bewildered Children

At this year's International English Spelling Bee For 10 Year Olds, the contest came down to four children. The judges decided to give each child two words to spell. No two children were given the ...
Truej's user avatar
  • 532
9 votes
4 answers
980 views

Murder Mystery. Who is the killer?

There is a riddle about a Murder Mystery. My friend, who is studying law, gave me this puzzle. It was originally given to him by his professor, who often gives puzzles to his students. There are 7 ...
Curiospire's user avatar
-2 votes
1 answer
117 views

Make numbers 1 - 30 using the digits 2, 0, 2, 5

Try to make all numbers 1-30 using the digits 2, 0, 2, 5. Rules: Use all four digits exactly once. Allowed operations: $+,−,×,÷,! \text{ (factorial)}, !! \text{ (double factorial)}, !!! \text{ (...
WOWOW's user avatar
  • 422
7 votes
2 answers
474 views

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 ...
Xavier Castillo's user avatar
-1 votes
1 answer
269 views

Benny, Denny, Kenny and Lenny: Who lies and who tells the truth?

To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you! ...
Will Octagon Gibson's user avatar
13 votes
3 answers
766 views

Mr. Martin And The Mismanaged Airport Terminal

There is a small international airport in Greece. It has just 6 gates, lined up from 1 to 6 going away from the front desk. Tickets here only have the last names of passengers and gate numbers clearly ...
Truej's user avatar
  • 532
4 votes
1 answer
282 views

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 ...
Sunny Lu's user avatar
  • 2,854
11 votes
1 answer
423 views

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 ...
Bernardo Recamán Santos's user avatar
4 votes
1 answer
371 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 "...
Sunny Lu's user avatar
  • 2,854
9 votes
1 answer
594 views

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 ...
Sunny Lu's user avatar
  • 2,854
16 votes
1 answer
740 views

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 ...
Jafe's user avatar
  • 77.8k
7 votes
1 answer
357 views

Proving that a particular order is impossible

A friend shared this puzzle with me on Discord: There are 5 bowls, labelled 1, 2, 3, 4 and 5. The bowls can only be moved around in pairs without changing the order of the pair. The bowls can also be ...
user avatar
2 votes
1 answer
154 views

Unique day of the year

I made this challenge. Astronomers announced that the sky and the moon will appear violet-velvet next week, and one of their workmates is also celebrating her birthday on the day that the moon will ...
Thirdy Yabata's user avatar
-1 votes
1 answer
155 views

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 ...
CrSb0001's user avatar
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