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I always start a Minesweeper puzzle on Windows Minesweeper by clicking the cell in the lower-left corner. Even though I have never seen a bomb there, how sound is this strategy? Is it possible that some time in the future there will be a bomb there? |
I always start a Minesweeper puzzle by clicking the cell in the lower left corner. Even though I have never seen a bomb there, how sound is this strategy? Is it possible that some time in the future there will be a bomb there? |
I always start a Minesweeper puzzle in Windows by clicking the cell in the lower left corner. Even though I have never seen a bomb there, how sound is this strategy? Is it possible that some time in the future there will be a bomb there? Or is it possible to click anywhere the first time? |
Is it always safe to click first in the lower lefthand corner of a Minesweeper puzzle? |
I've played many a-game of minesweeper, and I frequently reach positions in which there is no logical, deterministic way to come to a conclusion about how I should solve the puzzle.
How should I best approach solving these puzzles to guarantee the highest statistical victory?
> Meta-context: this question is an ... |
How do I approach a "stuck" game of minesweeper? |
Minesweeper, to those who do not know the strategies involved, is a difficult game.
How do I beat it every time, or at least with high frequency?
> Meta-context: [this question](http://puzzling.stackexchange.com/questions/357/how-do-i-win-minesweeper-every-time/358) is an offshoot of the current original question... |
What frequent patterns can be used to overcome Minesweeper obstacles? |
**Small notes**
- Remember that the number of remaining mines is the clue number minus the number of surrounding mines. This is important in patterns like 1-2-1; 3-2-3, for instance, also works if there are two mines next to each 3, since they both need 1 mine to be solved.
- A one by itself on a corner always in... |
In order to construct the solution to this problem in the general space, it's helpful to ignore the Grand Vizier. The Grand Vizier can hold all the keys except one, which all the slaves hold, and that answers that component minimally.
I have discovered a generic method for generating solutions to these puzzles given... |
Minesweeper, to those who do not know the strategies involved, is a difficult game.
What patterns exist in the game which I can take advantage of?
> Meta-context: [this question](http://puzzling.stackexchange.com/questions/357/how-do-i-win-minesweeper-every-time/358) is an offshoot of the current original questi... |
We have 1 ball on the table and 0 or 1 balls under a concealed cup. Now I ask you is the amount of balls on the table is larger than the number on your mind?
1. No, because 1 is not larger than the 1 or 2 balls on the table
2. Maybe, because maybe it's larger than 1, but it's not larger than 2
3. Yes, because ... |
![enter image description here][1]
Today I came across this puzzle:
> How many minutes is it until six o'clock if fifty minutes ago it was
> four times as many minutes past three o'clock?
Any help?
[1]: https://i.stack.imgur.com/kBk1l.png |
In Heinlein's _Space Cadet_, one of many tests administered to the protagonist seems to have no way of scoring any points. See the excerpt below.
> Late in the day he was ushered into a cubbyhole containing a chair, a gadget mounted on a desk, pencil and paper, and framed directions.
"If any score from a previous... |
Is it indeed impossible to score any points in the test in Heinlein's "Space Cadet"? |
How to solve Circular table problem? |
The question I would ask is this (where \$n\$ is the number you are thinking of):
> Is \$\lim_{x \to n} \frac{1}{x-2} > 0\$?
The possible answers are:
- If \$n = 1 \rightarrow \frac{1}{1-2} = -1\$, so the answer is **"No"**.
- If \$n = 2 \rightarrow \lim_{x \to 2} \frac{1}{x-2}\$, could be either \$+\infty\$ ... |
>"After the test starts," he read, "a score of T will result each time you press the lefthand button except as otherwise provided here below. Press the lefthand button whenever the red light appears provided the green light is not lighted as well except that no button should be pressed when the righthand gate is open u... |
> Alice goes into a toy store and asks the clerk, Bob, to help her pick out a toy. Alice tells Bob she needs a toy for one of the two kids of Carol, a friend of hers. Since Alice has only girls herself, she needs his help picking out a toy for a boy. Bob helps her find something and they chat a while.
> As a friendl... |
The following is a type of logic/math puzzle I've yet to see on this site. I feel it belongs because the kernel of this problem can be reworked into other puzzles. While I do not remember what the solution was, I remember vaguely the novel aspect of its analysis. I will solve it myself and provide the answer if no one... |
One classic puzzle has many different forms, but the basic strategy is the same.
> Once upon a time there was a crazy king who had a very wise minister
> with him. The king had a habit of playing a strange game on a circular table.
> The game was played as follows: The king told his minister a different number e... |
How to solve the circular table problem? |
How do you solve the circular table problem? |
The following is a type of logic/math puzzle I've yet to see on this site. I feel it belongs because the kernel of this problem can be reworked into other puzzles. While I do not remember what the solution was, I remember vaguely the novel aspect of its analysis. I will solve it myself and provide the answer if no one... |
The following is a type of logic/math puzzle I've yet to see on this site. I feel it belongs because the kernel of this problem can be reworked into other puzzles.
>\$N\$ pirates find themselves marooned on an island with no food stores, no other people, and no animal life besides one monkey. There are, however, ma... |
Is it better to start in a corner, edge, or any random middle square? If the first square isn't empty, when is it better to click a neighbor vs. another random square? How does the strategy vary by mine density?
By "optimal" I mean maximizing the probability of winning. |
> Today was "bring your kids to work"-day at the office. Alice has no kids of her own, but she saw her co-worker Bob with a lovely girl.
> "That's weird," she tought, "I thought he had two kids." So she approached them, asked the girl's name (Carol), and asked Bob if she was his only child.
> "Nah, " said Bob, "my ... |
The question I would ask is this (where \$n\$ is the number you are thinking of):
> Is \$\lim_{x \to n} \frac{1}{x-2} > 0\$ (where we are approaching \$n\$ from either the left or the right)?
The possible answers are:
- If \$n = 1\$: \$\frac{1}{1-2} = -1\$, so the answer is **"No"**.
- If \$n = 2\$: \$\lim_{x... |
As is the case with all information puzzles, we have to find away to map each outcome (yes, no, I don't know) to a different number (1, 2, 3). To do this, we need some property that's unknown for exactly one of these three numbers.
There are multiple ways to do this. The most basic (and most reliable) way would be t... |
[This question](http://puzzling.stackexchange.com/questions/313/you-have-one-question-to-tell-whether-the-number-im-thinking-of-is-1-2-or-3) requires a bit of logical distortion to get the information required to answer the question.
However, I've never seen it asked before what would happen if more modes of questio... |
[This question](http://puzzling.stackexchange.com/questions/313/you-have-one-question-to-tell-whether-the-number-im-thinking-of-is-1-2-or-3) requires a bit of logical distortion to get the information required to answer the question.
However, I've never seen it asked before what would happen if more modes of questio... |
The claim that this is the world's hardest sudoku puzzle was actually made by the author, and popularized by the media. There is nothing to suggest that this is the _singular hardest puzzle in existence_, however, it's still a pretty dern difficult puzzle.
To quote the author of the puzzle:
> "Normal sudoku puzzl... |
How do I solve the world's hardest sudoku? |
[This question](http://puzzling.stackexchange.com/questions/313/you-have-one-question-to-tell-whether-the-number-im-thinking-of-is-1-2-or-3) requires a bit of logical distortion to get the information required to answer the question.
However, I've never seen it asked before what would happen if more modes of questio... |
[This question](http://puzzling.stackexchange.com/questions/313/you-have-one-question-to-tell-whether-the-number-im-thinking-of-is-1-2-or-3) requires a bit of logical distortion to get the information required to answer the question.
However, I've never seen it asked before what would happen if more modes of questio... |
I'm thinking of a number, \$s\$, which equals either \$0\$ or \$1\$ with equal probability. If \$s=1\$, then \$p\$ is either \$0\$ or \$1\$ with an unknown probability distribution - otherwise \$p=0\$.
If your number is not four, is the \$\displaystyle\lim_{x\to n}\frac{1}{x-2-s-p}>0\$?
- If \$x=1\$, then the d... |
I'm thinking of a number, \$s\$, which equals either \$0\$ or \$1\$ with equal probability. If \$s=1\$, then \$p\$ is either \$0\$ or \$1\$ with an unknown probability distribution - otherwise \$p=0\$.
If your number \$n\neq 4\$, is the \$\displaystyle\lim_{x\to n}\frac{1}{x-2-s-p}\geq0\$?
- If \$x=1\$, then th... |
The claim that this is the world's hardest sudoku puzzle was actually made by the author, and popularized by the media. There is nothing to suggest that this is the _singular hardest puzzle in existence_, however, it's still a pretty dern difficult puzzle.
To quote the author of the puzzle:
> "Normal sudoku puzzl... |
> Bob walked into the clothing store. He looked a bit lost. "Hi, I'm Alice, can I help you?" said Alice. "Remember, you can get anything you want, at Alice's Restaurant." She looked at Bob again and swallowed her usual "excepting Alice."
>
> Bob laughed. "I was wondering about that name, but now I get the reference... |
> Today was "bring your kids to work"-day at the office. Alice has no kids of her own, but she saw her co-worker Bob with a lovely girl.
> "That's weird," she tought, "I thought he had two kids." So she approached them, asked the girl's name (Carol), and asked Bob if she was his only child.
> "Nah, " said Bob, "my ... |
> I'm thinking of a number, \$s\$, which equals either \$0\$ or \$1\$ with equal probability. If \$s=1\$, then \$p\$ is either \$0\$ or \$1\$ with an unknown probability distribution - otherwise \$p=0\$.
>
> If your number \$n\neq 4\$, is the \$\displaystyle\lim_{x\to n}\frac{1}{x-2-s-p}\geq0\$?
- If \$x=1\$, t... |
Assuming the game is played without cheating, in the [three-card monte](https://en.wikipedia.org/wiki/Three-card_Monte), can a logical approach increase the player's chance of beating the house?
At first glance it would seem to be unlikely but a [recent article in the BBC news](http://www.bbc.com/news/science-enviro... |
In the three-card monte, can a logical principle be applied to increase the odds? |
> I'm thinking of a number, \$s\$, which equals either \$0\$ or \$1\$ with equal probability. If \$s=1\$, then \$p\$ is either \$0\$ or \$1\$ with an unknown probability distribution - otherwise \$p=0\$.
>
> If your number is \$n\$, where \$n\neq 4\$, is the \$\displaystyle\lim_{x\to n}\frac{1}{x-2-s-p}\geq0\$?
... |
There is a classic problem below for which a very well written and thought out series of solutions can be found at: https://www.math.washington.edu/~morrow/336_11/papers/yisong.pdf
The variation here I've never seen anywhere but am curious. I want to work it out myself but think others may also want to give it a go.
... |
There is a classic problem below for which a very well written and thought out series of solutions can be found at: https://www.math.washington.edu/~morrow/336_11/papers/yisong.pdf
The variation here I've never seen anywhere but am curious. I want to work it out myself but think others may also want to give it a go.
... |
What is the lowest score you can get in 2048? For example, to fill up the space with the lowest numbers. |
What is the lowest you can get in 2048? |
There is a classic problem below for which a very well written and thought out series of solutions can be found at: https://www.math.washington.edu/~morrow/336_11/papers/yisong.pdf
The variation here I've never seen anywhere but am curious. I want to work it out myself but think others may also want to give it a go.
... |
What is the lowest score you can get in 2048? Creating high numbers is obviously bad, but what about not matching numbers? |
Number twenty-one cages containing mice, 1, 2, 3, etc., up to 21, and place them in the following order:
1 14 15 17 3 7 13 6 20 2 19 21 5 18 8 11 16 9 12 4 10
- You start from a cage of your choice, calling that cage *one*, and count, *one, two, three, etc.,* from left to right. Once you reach the end, ... |
The puzzle grid pictured below is a prime example of the classic rush to judgment:
![Minesweeper, all blown up][1]
[1]: https://i.stack.imgur.com/aELsO.png
I was so sure of my decision, but when I double-clicked to clear more cells, the cell to the left of the one I had just flagged (the red one next to th... |
How could I have avoided this mistake in Minesweeper? |
Number twenty-one cages containing mice, 1, 2, 3, etc., up to 21, and place them in the following order:
1 14 15 17 3 7 13 6 20 2 19 21 5 18 8 11 16 9 12 4 10
- You start from a cage of your choice, calling that cage *one*, and count, *one, two, three, etc.,* from left to right. Once you reach the end, ... |
What is the lowest score you can get in 2048? Creating high numbers is obviously bad, but what about not matching numbers?
What is the chance of getting this lowest score? |
[This question](http://puzzling.stackexchange.com/questions/371/how-do-you-solve-the-circular-table-problem) was asked about a group of people whom a king wishes to play a cruel game with. Going around in a circle, the king kills every other person.
The question concerned how one could compute the answer without ex... |
What is the solution to the generic round table problem? |
Can you tell me what is the name of the game I used to play in school?
It's a game for two players. You need grid paper and two pens.
The game is played on a 10x10 arena, shifted by half a grid to one side.
The players take turns, each drawing a one grid length line. One player plays "middles", the other plays... |
Can you tell me what is the name of the game I used to play in school?
It's a game for two players. You need grid paper and two pens.
The game is played on a 10x10 arena, shifted by half a grid to one side.
The players take turns, each drawing a one grid length line. One player plays "middles", the other plays... |
*The solution is **very** simple ones you know it. But may be you would like to give it a try first?*
The solution:
>! 1. The logicians numerate themselves (L1, L2, ..., LN) and colours (C1, C2, ..., CN).
>! 2. There are N equations:
>! 1) C1 + C2 + ... + CN mod N = 0
>! 2) C1 + C2 + ... ... |
Logic puzzles with a set of conditions and a "logic grid" are very popular. More than one publisher is currently producing puzzle books with these types of puzzles.
A Wikipedia article claims [Charles Lutwidge Dodgson, (*Lewis Carroll, author of Alice's Adventures in Wonderland.*)](https://en.wikipedia.org/wiki/Lo... |
When and where was the first logic-grid-based puzzle published? |
*The solution is **very** simple. The solution is very simple ones you know it. But may be you would like to give it a try first?*
The Solution:
1. The logicians numerate themselves (L1, L2, ..., LN) and colours (C1, C2, ..., CN).
2. There are N equations:
1) C1 + C2 + ... + CN mod N = 0
2) C... |
I came across the following interesting problem today:
> A game consists of a sequence of plays; on each play either you or your opponent scores a point, you with probability \$p < \frac{1}{2}\$, he with probability \$1-p\$. The number of plays is to be even (\$2, 4, 6, ...\$). To win the game, you must score *more ... |
I came across the following interesting problem today:
> A game consists of a sequence of plays; on each play either you or your opponent scores a point, you with probability \$p < \frac{1}{2}\$, he with probability \$1-p\$. The number of plays is to be even (\$2, 4, 6, ...\$). To win the game, you must score *more ... |
Let's look at the number of plays vs the number of games he has to win:
2: 2/2 + 1 = 2
4: 4/2 + 1 = 3
6: 6/2 + 1 = 4
n: n/2 + 1
Or in relative terms: 1, 3/4, 2/3, `1/2 + 1/n`. So the more they would play, the easier it would be for the first player to get more than half wins. This does not tak... |
When you're looking at a logical word puzzle, what sorts of clues should you try to look for to solve them? There have been quite a few puzzles posted to this site so far that I spent a few minutes pondering, and I just had no idea where to start. Once I saw the answers they usually made sense, but I don't seem to have... |
How do you solve a word puzzle when you have no idea where to start? |
As Ross already mentioned the first aha! moment should be when you realize that a prisoner can drink from multiple bottles. From this the next step is realizing that you can only perform the test once, so you cannot do separate tests based on the results of the previous test.
The key concept you should first realize... |
N logicians are wearing hats which can be of N different colors (each hat has one color; there can be multiple hats with the same color). Each logician can see the colors of all hats except his own. The logicians must simultaneously call out a color; they win if at least one logician calls the color of his own hat. The... |
As Ross already mentioned, the first aha! moment should be when you realize that a prisoner can drink from multiple bottles. From this the next step is realizing that you can only perform the test once, so you cannot do separate tests based on the results of the previous test.
The key concept you should first realiz... |
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". Centres of each face can also be handled as a 2x2x2 cube, ignoring the outer layers entirely.
Is it better to apply tho... |
*The solution is **very** simple. The solution is very simple ones you know it. But may be you would like to give it a try first?*
The Solution:
1. The logicians numerate themselves (L1, L2, ..., LN) and colours (C1, C2, ..., CN).
2. There are N equations:
1) C1 + C2 + ... + CN mod N = 0
2) C... |
*The solution is **very** simple. The solution is very simple ones you know it. But may be you would like to give it a try first?*
The Solution:
1. The logicians numerate themselves (L1, L2, ..., LN) and colours (C1, C2, ..., CN).
2. There are N equations:
1) C1 + C2 + ... + CN mod N = 0
2) C... |
*The solution is **very** simple. The solution is very simple ones you know it. But may be you would like to give it a try first?*
The Solution:
1. The logicians numerate themselves (L1, L2, ..., LN) and colours (C1, C2, ..., CN).
2. There are N equations:
1) C1 + C2 + ... + CN mod N = 0
2) C... |
I have been solving the Rubik's Cube 2x2x2, 3x3x3, 4x4x4 and 5x5x5, because things are very similar I though a 6x6x6 wouldn't be a challenge much. So I bought the C4U 3x3x7 see image. What I want to know is how to solve it, what algorithms do I need? I can't find any good YouTube tutorials and also not a good website w... |
Note that you need the same colours as on the 3x3x3, but with the 4x4x4 you can mix them up and later on while solving you have a problem when yours centers doesn't have the same colours as the 3x3x3.
1. Solve the centers:
- White Up, Red Front, Blue Right,
- Yellow opposite to White
- Red opposite t... |
Note that you need the same colours as on the 3x3x3, but with the 4x4x4 you can mix them up and later on while solving you have a problem when yours centers doesn't have the same colours as the 3x3x3.
1. Solve the centers:
- White Up, Red Front, Blue Right,
- Yellow opposite to White
- Red opposite ... |
**Notation** <br>
We need to have some notation for the algorithms. We use:
- \$U\$ for the upper layer and \$u\$ for the middle upper layer.
- \$R\$ for the right layer and \$r\$ for the middle right layer.
- \$L\$ for the right layer and \$l\$ for the middle left layer.
- \$?^2\$ for turning a layer twi... |
**Notation** <br>
We need to have some notation for the algorithms. We use:
- \$U\$ for the upper layer and \$u\$ for the middle upper layer.
- \$R\$ for the right layer and \$r\$ for the middle right layer.
- \$L\$ for the right layer and \$l\$ for the middle left layer.
- \$?^2\$ for turning a layer twi... |
**Notation** <br>
We need to have some notation for the algorithms. We use:
- \$U\$ for the upper layer and \$u\$ for the middle upper layer.
- \$R\$ for the right layer and \$r\$ for the middle right layer.
- \$L\$ for the right layer and \$l\$ for the middle left layer.
- \$F\$ for the front layer and \... |
*The solution is **very** simple. The solution is very simple ones you know it. But may be you would like to give it a try first?*
The Solution:
1. The logicians numerate themselves (L1, L2, ..., LN) and colours (C1, C2, ..., CN).
2. Let's introduce a new operation `%`, it's meaning please see below*. There are ... |
In a building, there is an odd elevator, which has only two buttons: UP, which makes it goes up 9 floors, and DOWN, which makes it goes down 7 floors. (Ground floor is floor 0). It is possible to reach each floor, but if the building was one floor less tall this would not be possible.
Which is the highest floor? |
**Notation** <br>
We need to have some notation for the algorithms. We use:
- \$U\$ for the upper layer and \$u\$ for the middle upper layer.
- \$R\$ for the right layer and \$r\$ for the middle right layer.
- \$L\$ for the right layer and \$l\$ for the middle left layer.
- \$F\$ for the front layer and \... |
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 don't necessarily line up with the other centers or nearby reference pieces, making it unclear as to when the pieces are s... |
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 don't necessarily line up with the other centers or nearby reference pieces, making it unclear as to when the pieces are s... |
**Notation** <br>
We need to have some notation for the algorithms. We use:
- \$U\$ for the upper layer and \$u\$ for the middle upper layer.
- \$R\$ for the right layer and \$r\$ for the middle right layer.
- \$L\$ for the right layer and \$l\$ for the middle left layer.
- \$F\$ for the front layer and \... |
As I've said in many other questions, puzzles like the one you posted are what I call *information puzzles* – that is, puzzles where you perform some trial to get as much information as possible about a certain unknown fact.
In this case, you can notice that each slave you use can either die or not die, which ... |
It seems like most word search puzzles have a quantity of words that match some theme, arraigned haphazardly, with some random letters filling in the extra spaces.
If I want to create and sell word search puzzles what do I need to consider in my puzzle creation? |
If I want to create word search puzzles what approach is best? |
**'Random' letters** <br>
Consider that the random letters you will up at the end are not truly random and you don't want them to be! If they are random they can form words that need to be found, in this way you can the puzzle more easy. You could also make the 'random letters' such that they form a word at the end, t... |
If you play two games, your chance is \$ p^2\$. If you play four, your chance is \$p^4+4p^3(1-p)\$, which becomes greater when \$p\gt \frac 13 \$. If you play six games, your chance is \$p^6+6p^5(1-p)+15p^4(1-p)^2\$, which is better than four games when \$p \gt \frac 25\$ It is tempting to conjecture that you shoul... |
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 and sell word search puzzles what do I need to consider in my puzzle creation? |
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 puzzles what do I need to consider in my puzzle creation? |
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 color touching (which takes an annoyingly long time to achieve). For example, this scramble is not a perfect one (showing the front face on... |
Is it possible to scramble a Rubik's cube such that no two squares of the same color are touching? |
Yes.
-
**Examples**:
- Superflip
- "Checkerboard"
 |
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 quarter of the way through a single 4x4 block, for example, when I realize that one of the words I'm about to create is tot... |
How do people decide which words to use in crossword puzzles? |
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