# Tag Info

Accepted

### Does the Rubik's Cube in this painting have a solved state?

Oo, this is a good one. Let's do some analysis: We can see the centres of three sides, and the relative positions of the centres cannot be changed, so we know that when/if this cube is solved, the ...
• 77.9k
Accepted

### Hotaru Beam Puzzle: Is it impossible?

Well so you could do Full solution (The "Try it online" link agrees that this is legal)
• 11.1k
Accepted

### Is there a puzzle that is only solvable by assuming there is a unique solution?

At least not if the solution space is a countable infinite set, or smaller. In that case, we can compute the finite time person 2) will need to find the solution found by person 1) by enumeration, ...
Accepted

### Barely Illegal Rubik's Cube State

We can see Therefore But the centre pieces tell us that Which is a contradiction. Therefore this cube cannot be solved.
• 7,770
Accepted

### Does this metal puzzle have a solution (Baguenaudier)

This puzzle is called a "Baguenaudier" which is French for "Time Waster". This solution assumes that you are holding the handle end on the left. The rings are numbered from right to left starting at ...
• 13.6k

### Solving "odd one out" problems. What am I doing wrong?

I can sympathize. This is from The Guardian, 2015: From left to right, starting with image 2, we have: no outline not a square green small leaving image 1 because it is the only image that is not ...
• 35.6k
Accepted

### Is this "Gear Turning" puzzle on Puzzlopia always solvable?

A random configuration of gears is solvable 1/3 of the time* For details on what kind of configuration is solvable, refer to the claim after the image below. Your hunch is right, we can use modular ...
• 6,042
Accepted

### General strategies for solving metal disentanglement puzzles

In the classic book "Winning Ways (for your mathematical plays)" by Berlekamp, Conway and Guy there is a small section devoted to wire puzzles (like the Tavern puzzles) in the second-to-last chapter. ...
• 54.2k

### Does this metal puzzle have a solution (Baguenaudier)

This can be solved in 16 steps. Lets use binary here, 0 is off, 1 is on the handle You start with 11111 1 - Remove the first ring to get 01111 2 - Remove the third ring to get 01011 3 - Put back the ...
• 60.7k

### Solving "odd one out" problems. What am I doing wrong?

The Situation that you are talking about is a lot more common than you know. And it's not only limited to odd-one-out puzzles. There are riddles which are basically "guess what I am thinking" puzzles. ...
• 15.2k
Accepted

### Is there an efficient algorithm for solving tiling puzzles?

Probably not. The bin-packing problem is NP-complete, and any instance of the bin-packing problem can be turned into a 2D packing problem. (Represent each integer $k$ with a $1\times k$ rectangle, and ...
• 148k

### Stuck on a puzzle

This puzzle is indeed broken, and has no solutions. (I ran into the same contradiction as Arnaud.) The organizer, Serkan YuÌˆrekli, made a post on the Logic Masters Deutschland forum around that time, ...
• 148k

### Is there a puzzle that is only solvable by assuming there is a unique solution?

No. If there is exactly one way to fill out the grid in a valid way, then that can be found without using any logic based on uniqueness. (It may be very painful, and require brute-forcing a lot, but ...
• 148k
Accepted

• 4,133
Accepted

### Is there a way in which all the members can be seated?

Here's a solution which explains the logic... First, you might find it useful to draw up a diagram like this, where every block of 16 letters represents a seat at the table (numbered 1 to 8 for ease ...
• 146k
Accepted

### Fill up a tetris field where bordering tiles have different colors

Shown here and in a tile formation Interpreted the even when rotated part of the question as just stating that a tetromino cannot touch the same colour tetromino ...
• 3,626
Accepted

### Strategies for solving steganography puzzles

This is how you can get started - Check out this article on Wikipedia which provides an insight. It also mentions some techniques used in Steganography. So, when you see a puzzle with ...
• 18.9k

### How many possible starting positions are uniquely solvable for a nonogram puzzle?

Absurdly partial answer Terminology: an "inner configuration" is an arrangement of filled and empty cells in our $n\times n$ grid; an "outer configuration" is the corresponding arrangement of run-...
• 120k
Accepted

### Best way to solve Codeword puzzle

Codeword puzzles are usually designed to have an approachable way of starting. (I am fairly sure it would be possible to make one that was solvable in principle but really hard to find one's way into, ...
• 120k

### Barely Illegal Rubik's Cube State

Here's one way to show the cube cannot be solved: Suppose the bottom face is white. Then the corner piece with yellow and white visible is in the right place, and is the fourth blue corner. That means ...
• 5,986
Accepted

### Can the rook pass every square just once?

The task is because An earlier version of the question didn't have the prohibition on diagonal moves. In that case because
• 120k
Accepted

### Can you solve the 7x7 (sudoku-ish) centered sums puzzle

This is quite easy to formulate as a 0-1 integer linear programming problem and then throw at a specialised solver. With no objective function to optimise, lp_solve ...
• 4,541

### Strategies for solving steganography puzzles

As Jan pointed out, a lot of it deals with finding hints in and around the puzzle. I just wanted to add additional strategies that I see being used in making and solving Steganography puzzles. ...
• 4,744
Accepted

### How to solve elastic band puzzles?

I've done a method to complete the first one and second one. Here is how I proceed Puzzle 1 Here is for puzzle 2! tricky one My idea for a global way of solving
• 2,700
Accepted

### $4\times4\times4$ Rubiks cube Top Layer Issue

It's a 4x4 Parity. The algorithm to solve is, $(2R)^2U^2(2R)^2u^2(2R)^2(2U)^2$ Where $2R$ is the second layer from right, $U$ is the top layer, $u$ is top two layers combined, $2U$ means second ...
• 3,943
Accepted

• 7,441

### Is there a way in which all the members can be seated?

• 14.7k
Find any integer $n$ such that $n$ is the number of solutions to this puzzle.