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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22
votes
0answers
2k views

Is there a move-efficient way to rotate the center pieces on the Octo-Star?

I'm looking for a more efficient algorithm to rotate the center column of the Octo-Star puzzle 45 degrees. The situation below occurs when four properly-oriented edges are next to each other, ...
4
votes
3answers
195 views

Filling a grid with skinny trominoes which have arrows on their ends

Let's have a 10x10 square grid with 7 empty small squares. This grid is to be filled with skinny trominoes which have arrows at their ends (see figure 1). What is the maximum number of arrows which ...
0
votes
0answers
43 views

IQ test question - squares, triangles, dots [closed]

I have this question from a friend. I suppose it is from a book. We have no idea where to start. Can someone help me with the correct answer, and what is the correct reasoning? Thank you!
10
votes
1answer
150 views

Pipelink: A Cat for jkittykitkat

Rules of Pipelink: Draw a loop through the centers of all cells. Two perpendicular line segments may intersect (cross) each other, but not turn at their intersection or otherwise overlap. Clues show ...
6
votes
4answers
651 views

Train Tracks: is there a unique solution?

In the last year or so a puzzle has been appearing in 'The Guardian' (a UK newspaper). It looks like this: and the instructions are as follows: Lay tracks to enable the train to travel from village ...
15
votes
2answers
728 views

Imagine a Sudoku with Text-Only: A Gridless 6x6 Antiknight Antidouble Sudoku

Imagine the following Sudoku: Imagine the Sudoku has a 6x6 grid with standard boxes, 2 rows and 3 columns each; and standard digits, 1 to 6. Imagine it has an antiknight rule: identical digits cannot ...
3
votes
2answers
264 views

A dance between numbers

Given the following equation: $$\Delta = \Biggl(\frac{t \mod 6}{(t \mod r) + 1}\Biggr)^2$$ Find the relationship between $t$ and $r$, along with the properties of each, that ensures $\Delta = 9$. For ...
8
votes
1answer
431 views

Can you reactivate a 4x4 Magic Square?

We've already removed the magic from a 3x3 magic square. Recently, one of our 4x4 magic squares was scrambled in an earthquake and I need your help to reactivate it's magic: Objective Your objective ...
1
vote
1answer
213 views

The maze of everlasting flowers

You were recently caught trespassing on the queen's hunting grounds. The punishment for this crime is a miserable experience the locals call the maze of everlasting flowers: The full resolution of ...
4
votes
1answer
327 views

A slightly different type of Sudoku puzzle

The following image shows two valid Sudokus. The first was copied verbatim off Wikipedia, and the second was obtained by rotating 90 degrees. Any two distinct valid Sudokus must differ in at least ...
2
votes
1answer
335 views

A number like waldo?

What is the smallest whole number that when its individual digits are summed, produces a number 4 digits long? For example, the number $5357$ is no where close since $5 + 3 + 5 + 7 = 20$. Note: I'm ...
8
votes
9answers
498 views

Infinite amount of theorems

We have an infinite amount of theorems $A_1, A_2 \ldots A_n$. Each one of the theorems says: "All of the following theorems are false.". Is there a single one of these theorems that is true?
11
votes
3answers
815 views

Historical figure sudoku

This sudoku hides a famous person from the past. A solution will be accepted if the sudoku is solved (with steps to solve). The letters used are: abceloprt (in alphabetical order). PS. ...
17
votes
3answers
427 views

Oh no, my puzzles are corrupted! What should I do? :(

This morning, I made three small and easy puzzles to be posted today. However, when I come back from my lunch, all of my puzzles are corrupted! :( The first one is a standard Curve Data puzzle. ...
7
votes
9answers
640 views

The Land of Truth and Lies [closed]

You live in The Land of Truth and Lies, where any of your statements may be inverted in meaning, without prior warning. For example, if you intend to say "You're looking good today", you may ...
3
votes
2answers
257 views

It's kind-of like Minesweeper

Have you ever played "Minesweeper" or "Lights Out!" and wondered what it would be like to reverse the process? Me too! Say hello to a 10 by 10 grid that I like to call "Number ...
20
votes
11answers
6k views

Who robbed the store?

You are investigating a shop robbery. The CCTV footage shows that there was one criminal, but it doesn't show their face. There are 10 suspects and you know that one of them is the criminal. The ...
11
votes
2answers
488 views

Confectionery Crime Conundrum

Yesterday I received one of the strangest cases of my career as an I.S. PI (Insightful Sleuths Private Investigator). I was reclining in my chair, working on the latest crossword puzzle when I ...
3
votes
1answer
178 views

Let's settle our differences

Can you complete this grid and expose the existing relationships? There are no complex operations (e.g. no exponents, square roots, functions, etc), additionally the numbers are all natural numbers ...
3
votes
2answers
328 views

Impasse with this Sudoku puzzle

This was an advanced puzzle, and I managed to take it as far as possible. Now, I am stuck. I have tried many advanced patterns to no avail. I could use some pointers. It's from an IOS app called &...
11
votes
2answers
766 views

Remove the magic from a 3x3 Magic Square

It's commonly stated that there is only one solution to the 3x3 magic square. This is simply because every variant found is simply a rotation, reflection or both of any other variant. Once such ...
14
votes
2answers
912 views

Some Stratospherically Strenuous Sudoku

These three sudoku are particularly irksome, can you logically deduce the solutions to all (or any!) ...and provide your reasoning? They are all proper sudoku - each has a unique solution. They can, ...
8
votes
2answers
173 views

Orthogonal Sudokus

This a Sudoku puzzle created by Paul Vaderlind. Fill each cell with 2-digit numbers from 11 to 99 (without the digit 0) such that The first digits represent one regular Sudoku grid. The second digits ...
6
votes
3answers
861 views

Help solving this sudoku?

I went up in difficulty on my Sudoku app (Enjoy Sudoku app on Android). I keep getting mostly through them; however, I keep getting stuck towards the end of the puzzle. An example is shown below. Can ...
3
votes
2answers
263 views

Fix this puzzle, please!

My students claim that this disconnect four puzzle (fill the grid with crosses and zeros, such that no four equal symbols appear in a row. Rows can be horizontal, vertical, or diagonal) does not have ...
12
votes
1answer
257 views

KPK 2021 Leftover: Double Back (Little Killer)

Rules of Double Back: Draw a non-intersecting loop through the centers of all empty cells. The loop passes through each region exactly twice. These two puzzles are the leftover of KPK 2021. The ...
8
votes
1answer
125 views

Trichain: Tetrachain

This is a Trichain puzzle. The rules of Trichain are as follows: Numbers must be white, and match the size of their white islands. Each white island can only contain at most one number. Some white ...
2
votes
0answers
84 views

Most leads in a "difficult" Sudoku

Since "difficult" is undefined, let me define it arbitrarily: A Sudoku is difficult if it can't be solved by only considering singles (naked or hidden), the most basic solving strategy. How ...
31
votes
2answers
3k views

Sudoku on a Mobius Strip

Well we've done sudoku on keyboards, so the next step is obviously putting a Sudoku on a Mobius strip... of course... I present, the world's very first MOBIUS SUDOKU: Now this sudoku is going to be a ...
1
vote
1answer
80 views

How to solve the syllogism problem [closed]

Two statements are given below followed by two conclusions, I and II. You have to consider the statements to be true even if they seem to be at variance from commonly known facts. You have to choose ...
-2
votes
1answer
148 views

Logical statements relating being sunny, wet, windy, having a raincoat, and sweating [closed]

How do I solve the following? If it is sunny, I am wet. If I wear a raincoat, I sweat. When it rains, there is no sun, but I am dry; and when there is wind and no sun, my sweat evaporates. In a rainy ...
2
votes
2answers
283 views

Blue eyes riddle: a counter-argument to accepted solution

I would like help understanding my flawed logic in my following reasoning: The Blue-eyes Riddle is commonly expressed as A group of people with assorted eye colors live on an island. They are all ...
19
votes
1answer
808 views

Tapata (Tapa variation)

Rules: Shade some cells so that all shaded cell form one orthogonally connected area. Numbered cells are either tapa clue (represent the lengths of the shaded cell surrounding that clue) or pata clue ...
20
votes
1answer
835 views

HAISU with a twist

HAISU is a grid-deduction puzzle designed by this site's very own TheGreatEscaper. To quote them: HAISU is a portmanteau of three Japanese words - 'hairu', to enter, 'su', number, and 'hausu', an ...
1
vote
4answers
5k views

Fill 3x3 magic square with distinct numbers 1..60 summing up to 69

I have to fill a whole 3x3 grid in such a way that the sum of each row, column, and main diagonal is 69. I couldn't find any logic to fill it up. I have to use distinct numbers from 1 to 60 for this. ...
0
votes
1answer
110 views

Does every validly posed Sudoku have at least one solution and if not what is the minimum number of givens for it to be unsolvable? [duplicate]

Does every validly posed Sudoku (doesn't break any Sudoku rules so only no duplicate 1 to 9 in rows, columns or square) have at least one solution, and if not, what is the minimum number of givens for ...
5
votes
4answers
1k views

Figure matrix IQ Problem

Found an old IQ problem that came up in an earlier job search. Still don't know how to solve it. I tried counting the number of edges/ faces and flipping the diagrams, but I can't see the trick.
1
vote
1answer
137 views

Divide a board into two pieces without cutting a domino

Saw this question in the book, "A Moscow Math circle" by Dorichenko. Eighteen 2x1 dominoes cover a 6x6 board without overlapping each other or the sides of the board. Prove that, for any ...
1
vote
1answer
217 views

The Turing Test "It doesn't Add Up question"

In the square below, change the position of six numbers, one per horizontal row, vertical column and long diagonal line of six smaller squares, in such a way so the numbers in each row, column or ...
17
votes
4answers
1k views

It's a LITS! And a... um...?

I've combined two of my favourite puzzle types - a LITS grid-deduction puzzle and a, er... a, um... you know, I could have sworn I wrote it down here somewhere! Click on the image for a resolution ...
112
votes
16answers
1.3m views

Two doors with two guards - one lies, one tells the truth

You are a prisoner in a room with 2 doors and 2 guards. One of the doors will guide you to freedom and behind the other is a hangman–you don't know which is which. One of the guards always tells the ...
9
votes
1answer
1k views

Strategies for Circuit Board Puzzle from NYT

The New York Times publishes a collection of variety puzzles each week, and new to the rotation recently is one called "Circuit Board". Here is an example of a puzzle (I added coordinates ...
3
votes
1answer
152 views

How many Hoshi (Star Sudoku) are possible?

A gifted Sudoku booklet's Hoshi are (almost? - I did only spot checks) all identical, except for number permutation and leads. An excuse for this would be if there were only one legit Hoshi. How many ...
3
votes
8answers
665 views

5 logicians with 1 or 2 hats (Part II) [8,9,10]

This is the corrected version of this question. There are 5 logicians seated around a table. They are blindfolded and hats are placed on their heads. After removing the blindfolds, they are told a ...
15
votes
1answer
869 views

9x9 Vanilla Tapa

Rules of Tapa: Shade some cells so that all shaded cells form one orthogonally connected area. Clues cannot be shaded and represent the lengths of the shaded cell surrounding that clue. If there are ...
6
votes
6answers
1k views

Five logicians with one or two hats [7,8,9]

There are five logicians seated around a table. They are blindfolded and hats are placed on their heads. After removing the blindfolds, they are told a true statement: Each of you has either one hat ...
2
votes
1answer
227 views

Mysterious Deaths, or is it just a well known attack?

Last week you were promoted to the position of Sergeant Head Detective of Australia, which basically means the best detective in Australia. Its January 2019, and you wake up ready for your new job. ...
19
votes
3answers
2k views

The Thieves and the Gold Bars

Two thieves (Rod and Lia) carry out a big heist and steal 16 gold bars. They get away in their car when they run into a bad accident and the car is completely wrecked. Luckily they survive with their ...
18
votes
7answers
4k views

Logical puzzle from a math homework for Russian fifth-year school students

The daughter of a relative of mine, a fifth-year school student in Russia, got the following math homework from her teacher: Here's my translation: Logical task No. 26. Students were solving a task ...
0
votes
2answers
157 views

How many liars were there at the party? [duplicate]

Andy’s birthday party has just been moved up by a week. All the toys in Andy’s room are worried about being replaced by fancy new toys. Sheriff Woody, Andy’s favourite toy, and the others are waiting ...

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