79 votes
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 ...
Bass's user avatar
  • 77.4k
32 votes
Accepted

Hotaru Beam Puzzle: Is it impossible?

Well so you could do Full solution (The "Try it online" link agrees that this is legal)
Lukas Rotter's user avatar
  • 10.3k
25 votes
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, ...
SE - stop firing the good guys's user avatar
25 votes
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.
happystar's user avatar
  • 7,566
22 votes
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 ...
LeppyR64's user avatar
  • 13.6k
21 votes

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 ...
JMP's user avatar
  • 35.6k
20 votes
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 ...
justhalf's user avatar
  • 6,034
20 votes
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. ...
Jaap Scherphuis's user avatar
17 votes

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 ...
Beastly Gerbil's user avatar
12 votes

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. ...
Sid's user avatar
  • 15.2k
12 votes
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 ...
Deusovi's user avatar
  • 146k
11 votes

Stuck on a puzzle

This puzzle is indeed broken, and has no solutions. (I ran into the same contradiction as Arnaud.) The organizer, Serkan Yürekli, made a post on the Logic Masters Deutschland forum around that time, ...
Deusovi's user avatar
  • 146k
11 votes

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 ...
Deusovi's user avatar
  • 146k
10 votes
Accepted

Does AAA+BBB+CCC+DDD=ABCD have a solution for distinct digits A,B,C,D?

The answer is: Because:
wythagoras's user avatar
  • 4,133
10 votes
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 ...
Stiv's user avatar
  • 142k
9 votes
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 ...
gtwebb's user avatar
  • 3,626
9 votes
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 ...
Techidiot's user avatar
  • 18.9k
9 votes

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-...
Gareth McCaughan's user avatar
9 votes
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, ...
Gareth McCaughan's user avatar
9 votes

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 ...
Rob Watts's user avatar
  • 5,966
8 votes
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 ...
Peter Taylor's user avatar
  • 4,541
8 votes
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
Gareth McCaughan's user avatar
8 votes

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. ...
n_plum's user avatar
  • 4,744
8 votes
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
Untitpoi's user avatar
  • 2,700
8 votes
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 ...
19aksh's user avatar
  • 3,933
8 votes
Accepted

Stuck on a puzzle

Arnaud Mortier's user avatar
8 votes

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

My answer is
Weather Vane's user avatar
  • 14.4k
8 votes

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

Find any integer $n$ such that $n$ is the number of solutions to this puzzle.
Marc-André Brochu's user avatar
8 votes
Accepted

What is the name & solution for this 33-piece 3D wooden puzzle?

This appears to be the Hercules burr puzzle. (It may also be known as Diamond #33; I can't tell if theirs is the same, because they claim to have 9 different shapes but they also don't cut the corners....
Deusovi's user avatar
  • 146k

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