# All Questions

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### How many Queens and Knights does it take to cover a chessboard?

Given an 8x8 chessboard, your goal is to "cover" each space on the board. A space is "covered" if there is a piece on it, or if a piece on the board can be moved to that space in one move. If you ...
731 views

### Find the color of the chess pieces

The colors of the pieces in the diagram is unknown. The diagram can be obtained from a real game. One needs to find the color of each piece: Black or White. I do not know the full solution. It is ...
738 views

### What is the expected length of the longest piece?

If a rod of unit length is broken into $n$ pieces, what is the expected length of the longest piece? The positions at which the rod is broken are chosen randomly uniformly. This is a generalization ...
3k views

### Knights and jokers

There are $N$ men. $K$ of them are knights, $M$ of them are jokers. $N$ is known, $K$ and $M$ are unknown. You know that: $K + M = N$, $K \gt M$, $M \ge 1$, $N$ is odd. Knights always tell the truth, ...
736 views

### Identify unique Verbal Arithmetic Puzzles

I am attempting to create original Verbal Arithmetic puzzles such as the famous one from this question Alphametic (Verbal Arithmetic) general strategy : SEND+MORE=MONEY For these problems each ...
2k views

### How to create a pure mathematical-logical based puzzle equivalent to resistance based physical puzzle?

I am thinking how to reformulate a physical puzzle in a way that it becomes purely logic based (doesn't uses physical lows and can be solved by a person, who knows nothing about physics). The puzzle: ...
844 views

### Is there a retrograde analysis puzzle like "Point on the incorrectly drawn chess piece"?

Does anybody know a nice chess puzzle, where the question states: Exactly one piece is drawn incorrectly on this diagram; another piece must be drawn on its position. Find the incorrectly drawn ...
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, ...
73k views

### Which way is the bus going?

If I'm not mistaken, this is a children's puzzle, but it got me thinking for a while. The bus is driving on the autobahn. Relative to you, which way is the bus going? Left or Right?
31k views

### How can I solve the Gear Cube Extreme?

The Gear Cube Extreme is another Mechanical Puzzle. I ordered it not so long ago and a friend of mine "accidentally" scrambled it. Now I want to solve it again but I have no idea how or even where to ...
7k views

### Is there any way to 'trap' my opponent on Connect Four?

I am trying to find out if there are any 'optimal' moves in the game, so as to trap my enemy to put his pawns in the place where I need them
2k views

### 5x5x5 Rubik's Cube Smiley

I did some turning on my 5x5x5 Rubik's Cube and I now have the cube like on the image below. 4 times a smiley -_- and 2 times a solved plane. But I have no idea how ...
3k views

### Is there a rating system for crossword puzzles?

On searching the internet for difficult crossword puzzles I find that the New York Times is often mentioned. But is there a rating system? If so how does it work?
4k views

### Why must a sudoku have a unique solution [closed]

Why must a sudoku have a unique solution. In my books I don't guarantee it. But I am sure there are not many which don't. I doubt if one in a thousand dont have. And even if they don't its only a ...
3k views

### What chess position has the longest string of moves before mate?

In chess puzzles, the objective of the puzzle is usually to checkmate the opponent using some form of novel strategy or tactic. For example, this puzzle from chess.com has white to play and mate in ...
3k views

### Fastest way to collect an arbitrary army

I am looking for solution of this puzzle: There is a kingdom with a square shape with sides of length 1. The castle is located at the center of the square. At the castle the king lives under the ...
161k views

### Clever ways to solve Mastermind?

Is there any specific way to solve Mastermind? Apart from the first step that is pure chance, is there any way to continue based on the colors that you think are correct?
240 views

### How does one make a program to provide all the 'possible' numbers in an empty cell

To be able to solve a sudoku one usually has to first work out all the 'possible' numbers in an empty cell. How can one make a program to do this? In this case 'possible numbers' are ones which have ...
4k views

### How many distinct unsolvable Rubik's cubes exist?

I wanted to answer this question: Why can't I have only one edge piece flipped on a 3X3 Rubik's cube? by saying that it is homomorphic to the illegal state in this question: Why is a ...
1k views

### Odds of duplicate birthdays

I found the following problem in an number of places online: John once bet a fellow gambler that two of the first thirty persons they met and spoke to would prove to have the same birthday. Strong in ...
3k views

### Why can't I have only one edge piece flipped on a 3X3 Rubik's cube? [duplicate]

I was using the beginner method to deliberately solve a 3X3 cube with one edge piece flipped. But, by the time I got to the top I discovered that I couldn't solve it with only one edge flipped. I had ...
2k views

### The Magic Stick

Here's a relatively easy puzzle that's actually entirely my own creation. An old guru in an Asian monastery is showing his beloved student his gallery of items that he has either collected or kept ...
680 views

### Cryptic clue "Injured person's mostly easy-going (8)"

I'm stumped on the last clue in another cryptic crossword. The clue is Injured person's mostly easy-going The (confirmed) cross-clues give C_S_A_T_. Normally I can guess at a part or at least the ...
550 views

### What is "A non-PC American woman overseas?"

I'm stuck on the last clue of a cryptic crossword. The clue is: A non-PC American woman overseas? (6) The cross letters are A_R_A_, confirmed by "check answers." Cryptic Crosswords iPhone app, ...
267 views

### Is there any specific way to play Solitaire?

I am interested in finding out if there is any specific way (algorithm) to play solitaire (not the card game)
420 views

### Mean to confine flower that's fibrous (7)

From the Guardian Cryptic crossword No 26,271, set by Chifonie: Mean to confine flower that's fibrous (7) The confirmed answer is I can see the definition, and I think part of the wordplay, but ...
9k views

### Aside from brute force, how can I solve this puzzle?

Once upon a time, and old lady went to sell her vast quantity of eggs at the local market. When asked how many she had, she replied: Son, I can't count past 100 but I know that: If you ...
223 views

### What are the odds that there is no solution on a given Set board?

I was playing a game of Set with a group. We had the usual twelve cards out and all agreed that there was no set. We then increased the number of cards to fifteen and were still unable to find a set....
2k views

### How to solve Oskar van Deventer's gear maze 2x2

One of Oskar van Deventer's puzzles is the gear maze 2x2.There are 4 gears connected together so if you move one gear all four gears rotate (two clockwise, the other two counter-clockwise).On the ...
992 views

### Are there any puzzle/solitaire games based on chess?

First, I apologise for asking a question that's not strictly in the right Q&A format; I'm hoping there are quality answers anyway. Are there any puzzle or solitaire games based on chess? By this ...
6k views

### Is there an algorithm for the Rubik's 360?

Is there an algorithm to help me solve the Rubik's 360? Usually I just do it at random, but I rarely succeed.
1k views

### Are there any popular puzzles with polynomial-time algorithms?

First, a little background: as I noted in my answer to another question here, most of the puzzles that seem to stay popular for extended periods of time are canonically 'hard' in an algorithmic sense: ...
1k views

### How many digits can be removed from a multiplication puzzle and still give only one answer?

There's a common category of mathematical puzzle which involves determining missing numbers in a long multiplication problem. As an example from this site (problem 10): ...
4k views

### How many squares can 4 queens control?

Though there is no strict mathematical proof, it has been shown via brute-force that no arrangement of 4 or fewer queens can control every square on a standard 8x8 chessboard. So, out of the 64 ...
689 views

### What size of puzzle is appropriate?

I am making a puzzle based on a Project Euler problem. Here is the puzzle at present: What path in the triangle below, starting from the top number with each step moving to one adjacent number in ...
22k views

### Why does this solution guarantee that the prince knocks on the right door to find the princess?

I found this puzzle online: On the top floor of a castle lives a princess. The floor has 17 bedrooms arranged in a row. Each bedroom has doors connecting to the adjoining bedrooms as well as to the ...
2k views

### What kind of glues are not conducive to long-term puzzle preservation?

If one has a very large puzzle of an image that one desires to mount and frame; what kind of glues would damage the puzzle piece over time? I have heard of 'puzzle glues', but question if this is ...
1k views

### How Random does a 3x3x3 (or other rubik cubes) need to be in speed solving?

Is there a rule/method to know how "random" should the cube be when solving it? in order for it to be a "valid" score?
2k views

### What is the Rush Hour puzzle with the most steps in its solution?

Rush Hour is a well-known sliding-block puzzle in which you push cars around (each car moves horizontally or vertically) to let a red car escape the grid. The standard board is a 6x6 grid, with four ...
520 views

### What are the conventions telegraphing when answers are abbreviated in New York Times crosswords?

There are a number of conventions you can count on fairly consistently in the New York Times crossword. One is that abbreviated answers are "signaled" somehow - an answer that is an acronym/...
2k views

### Why is "trapeze" the solution to this cryptic crossword clue?

I was doing a cryptic crossword this morning and I came across the following clue: Circus equipment has chimpanzee, say at the centre The answer is "TRAPEZE" (confirmed by "check answers"). The ...
873 views

### How do people decide which words to use in crossword puzzles?

I've tried my hand at creating a crossword a few times, but generally there have been way too many interlinks between words for me to create even a solution grid with any ease. Often I get about a ...
22k views

### Is it possible to scramble a Rubik's cube such that no two squares of the same color are touching?

My friend always insists on scrambling my Rubik's cube "perfectly" before giving it to me to solve. According to his definition, a "perfect" scramble must have no three of the same ...
2k views

### If I want to create word search puzzles what approach is best?

It seems like most word search puzzles have a quantity of words that match some theme, arranged haphazardly, with some random letters filling in the extra spaces. If I want to create word search ...
20k views

### Where should I start on the Ghost Cube?

The Ghost Cube is a 3x3 shape modification which is solved when two layers are rotated out of position. As a result, in order to solve the puzzles, you need to move pieces into positions where they ...
931 views

### A building with an odd elevator

In a building, there is an odd elevator, which has only two buttons: UP, which makes it go up 9 floors, and DOWN, which makes it go down 7 floors. (The ground floor is floor 0.) It is possible to ...
3k views

### How do I solve the C4Y 3x3x7?

I have been solving the Rubik's Cube 2x2x2, 3x3x3, 4x4x4 and 5x5x5, and because things are very similar I thought a 6x6x6 wouldn't be a challenge much. So I bought the C4U 3x3x7 - see image. What I ...
2k views

### 4x4x4 Rubiks Cube strategy

With a 4x4x4 cube, it's possible to apply the same strategies as for a 3x3x3, either treating it as a 3x3x3 with a double-width middle or else as a 2x2x2 and just working on the corner "quadrants". ...