instruction stringlengths 15 30k |
|---|
Does anybody know a nice chess puzzle, where question states: "Exactly one piece is drawn incorrectly on this position. Find which one."? One needs to make retrograde analysis of the given position and find, which from all pieces is drawn incorrectly.
I really would like to find such a puzzle.
_____________
P.S... |
Is there retrograde analysis puzzle like "Point on the incorrectly drawn chess piece"? |
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:
> The electric circuit in the image is made from the infinite number of wire-frame-squares. The next square is exa... |
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:
> The electric circuit in the image is made from the infinite number of wire-frame-squares. The next square is exa... |
Does anybody know a nice chess puzzle, where question states: "Exactly one piece is drawn incorrectly on this position. Find which one."? One needs to make retrograde analysis of the given position and find, which from all pieces is drawn incorrectly.
I really would like to find such a puzzle.
_____________
P.S... |
Does anybody know a nice chess puzzle, where question states: "Exactly one piece is drawn incorrectly on this diagram, another piece must be drawn on it's position. Find incorrectly drawn piece."? One needs to make retrograde analysis of the given position and find, which from all pieces is drawn incorrectly.
I real... |
I am attempting to create original Verbal Arithmetic puzzles such as the famous one from this question http://puzzling.stackexchange.com/questions/51/verbal-arithmetic-general-strategy
:
SEND+MORE=MONEY
For these problems each letter represents a different one digit number but the equation still holds true. Th... |
20 teams played a round robin tournament. The winner of each game got 1 point, the loser none, there were no draws. Each team's total score was a square number. At least one team had a unique score. How many upsets were there, defined as times a team with a lower total score beat a team with a higher total score? ... |
Let's put the number of coins at \$c\$ and see what happens if we increase \$n\$. We'll number the pirates from meekest (\$1\$) to fiercest (\$n\$).
\$\begin{array}{rrrll}
\begin{array}{c}\text{Nr. of pirates}\end{array} &
\begin{array}{c}\text{Pirate} \\ \text{meekest to fiercest}\end{array} &
\begin{arra... |
If you flip that many coins, will you get two the same? |
> There are 101 men. Some of them are knights, the others are jokers. Knights always tell truth, jokers can tell whatever they want. There are more knights then jokers and all 101 people know who is who. You go to anyone of them and ask him a yes-or-no question. You can repeat this procedure number of times with the sa... |
> There are 101 men. Some of them are knights, the others are jokers. Knights always tell truth, jokers can tell whatever they want. There are more knights then jokers and all 101 people know who is who. You go to anyone of them and ask him a yes-or-no question. You can repeat this procedure number of times with the sa... |
> There are N men. K of them are knights, M of them are jokers.
> K + M = N, K > M, N is odd.
> Knights always tell truth, jokers can tell whatever they want. All N people know who is who. You go to anyone of them and ask him a yes-or-no question. You can repeat this procedure number of times with the same man ... |
> There are N men. K of them are knights, M of them are jokers.
> K + M = N, K > M, M >= 1, N is odd.
> Knights always tell truth, jokers can tell whatever they want. All N people know who is who. You go to anyone of them and ask him a yes-or-no question. You can repeat this procedure number of times with the s... |
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:
> The electric circuit in the image is made from the infinite number of wire-frame-squares. The next square is exa... |
> There are N men. K of them are knights, M of them are jokers.
> K + M = N, K > M, M >= 1, N is odd.
> Knights always tell truth, jokers can tell whatever they want. All N people know who is who. You go to anyone of them and ask him a yes-or-no question. You can repeat this procedure number of times with the s... |
Here's a generalization of a puzzle I recently encountered, the answer to which I do not know myself:
> 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. |
What is the expected length of the longest piece? |
Does anybody know a nice chess puzzle, where question states: "Exactly one piece is drawn incorrectly on this diagram, another piece must be drawn on it's position. Find incorrectly drawn piece."? One needs to make retrograde analysis of the given position and find, which from all pieces is drawn incorrectly.
I real... |
Does anybody know a nice chess puzzle, where question states: "Exactly one piece is drawn incorrectly on this diagram, another piece must be drawn on it's position. Find incorrectly drawn piece."? One needs to make retrograde analysis of the given position and find, which from all pieces is drawn incorrectly.
I real... |
> There are N men. K of them are knights, M of them are jokers.
> K + M = N, K > M, M >= 1, N is odd.
> Knights always tell truth, jokers can tell whatever they want. All N people know who is who. You go to anyone of them and ask him a yes-or-no question. You can repeat this procedure number of times with the sa... |
> There are N men. K of them are knights, M of them are jokers.
> N is know, K and M are unknown. You know that: K + M = N, K > M, M >= 1, N is odd.
> Knights always tell truth, jokers can tell whatever they want. All N people know who is who. You go to anyone of them and ask him a yes-or-no question. You can re... |
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 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 we... |
How do I solve the C4Y 3x3x7? |
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 have n Queens, what is the minimum number of added Knights you have to have to do this?
Can we solve this for n = 1, ... |
How many Queens and Knights does it take to cover a chessboard? |
If you flip that many coins, will you get two the same?
As Doorknob put it... "1 => no, because it's only one, 2 => maybe, because it could be one of TH, HT, TT, or HH, 3 => yes, because a coin flip has only two possible outcomes" |
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 have n Queens, what is the minimum number of added Knights you have to have to do this?
Can we solve this for n = 1, ... |
> 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 > M\$, \$M >= 1\$, \$N\$ is odd.
> Knights always tell the truth, jokers can tell whatever they want. All N people know who is who. You go to anyone of them... |
> Colours of the pieces on the diagram is unknown. One needs to find colour of each piece: Black or White.
>![enter image description here][1]
I do not know the full solution.
It is easy to find colors of the most pieces:
>! 1. The kings should not be checkmated by pawns (otherwise what was the previous move... |
I'm thinking about the following strategy for http://puzzling.stackexchange.com/questions/548/fastest-way-to-collect-an-arbitrary-army:
1. When solder decides to go to some house he "reserves" it.
2. Ones solder is free (has delivered the news to another house) he takes the closest house from all unreserved and goe... |
Does this strategy works? |
I'm thinking about the following strategy for http://puzzling.stackexchange.com/questions/548/fastest-way-to-collect-an-arbitrary-army:
1. When solder decides to go to some house he "reserves" it.
2. Ones solder is free (has delivered the news to another house) he takes the closest house from all unreserved and goe... |
> Colours of the pieces on the diagram is unknown. The diagram can be obtained in real game. One needs to find colour of each piece: Black or White.
>![enter image description here][1]
I do not know the full solution.
It is easy to find colors of the most pieces:
>! 1. The kings should not be checkmated by p... |
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 have *n* Queens, what is the minimum number of added Knights you have to have to do this?
Can we solve this for *n = ... |
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 have \$n\$ Queens, what is the minimum number of added Knights you have to have to do this?
Can we solve this for \$n... |
I am looking for hints to find the solution of this puzzle:
> There kingdom with a square shape with sides of length 1. The castle is located in the center. At the castle the king lives under the protection of one soldier. There are other solders; each solder is at his own house. Houses are spread throughout the are... |
Does this strategy work? |
I've made some progress by looking at the number of captures (7) vs the number of pawns that have changed file. The extra f pawns can't have come from the left in only seven captures, so we should have four captures bringing them from the right.
h->g x2
g->f x2
The extra d pawn must have come from the left, so we ge... |
I've already shown how you can force my other answer to fail. Hopefully this one will not have such an exploit.
- Step 1: First knight goes to the extreme house on the map.
(Equivalent to just going the the north house if there is a house
there.) (Maximum time \$\frac{\sqrt{2}}{2}\$) For a sometimes faste... |
> 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 > M\$, \$M >= 1\$, \$N\$ is odd.
> Knights always tell the truth, jokers can tell whatever they want. All N people know who is who. You go to anyone of them... |
I've already shown how you can force my other answer to fail. Hopefully this one will not have such an exploit.
- Step 1: First knight goes to the extreme house on the map.
(Equivalent to just going the the north house if there is a house
there.) (Maximum time \$\frac{\sqrt{2}}{2}\$) For a sometimes faste... |
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 have \$n\$ Queens, what is the minimum number of added Knights you have to have to do this?
Can we solve this for \$n... |
I want to create a Sudoku puzzle, and I want it to be of moderate difficulty.
There's a specific pattern I want to include, called the X-Wing pattern:
> ![enter image description here][1] ![enter image description here][2]
This occurs when two numbers form locked pairs - the two squares are the only ones of a ... |
How do I necessitate the use of the X-Wing pattern during Sudoku creation? |
In Wikipedia's bibliography of [Martin Kruskal][1] it is said:
> Martin, who had a great love of games, puzzles, and word play of all
> kinds, also invented several quite unusual origami models including an
> envelope for sending secret messages (anyone who unfolded the envelope
> to read the message would have g... |
In Wikipedia's bibliography of [Martin Kruskal][1] it is said:
> Martin, who had a great love of games, puzzles, and word play of all
> kinds, also invented several quite unusual origami models including an
> envelope for sending secret messages (anyone who unfolded the envelope
> to read the message would have g... |
I've made some progress by looking at the number of captures (7) vs the number of pawns that have changed file. The extra f pawns can't have come from the left in only seven captures, so we should have four captures bringing them from the right.
h->g x2
g->f x2
The extra d pawn must have come from the left, so we ge... |
> 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 > M\$, \$M >= 1\$, \$N\$ is odd.
> Knights always tell the truth, jokers can tell whatever they want. All N people know who is who. You go to anyone of them... |
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 have \$n\$ Queens, what is the minimum number of added Knights you have to have to do this?
Can we solve this for \$n... |
> How do you write 23 using only the number 2?<br /> 34 using only the
> number 3?<br /> 56 using only the number 5?<br /> 100 using only the
> number 9?<br />
You can use only the numbers said, but any math you want in order to get the wanted result |
I've made some progress by looking at the number of captures (7) vs the number of pawns that have changed file. The extra f pawns can't have come from the left in only seven captures, so we should have four captures bringing them from the right.
h->g x2
g->f x2
The extra d pawn must have come from the left, so we ge... |
There is a puzzle:
> Each of the two spies must pass another one secret numbers (one per spy) unnoticed for enemies. They agreed on a way to do it in advance and today they come to the river, where lies a bunch of 26 identical stones, and to throw stones into the water. First one throws a group of stones, then secon... |
What are maximum numbers two spies can exchange? |
There is a puzzle:
> Each of the two spies must pass another one secret numbers (one per spy) unnoticed for enemies. They agreed on a way to do it in advance and today they come to the river, where lies a bunch of 26 identical stones, and to throw stones into the water. First one throws a group of stones, then secon... |
There is a puzzle, which is defined in the title shortly:
> Each of the two spies must pass another one secret numbers (one per spy) unnoticed for enemies. They agreed on a way to do it in advance and today they come to the river, where lies a bunch of 26 identical stones, and to throw stones into the water. First o... |
What are the maximum numbers two spies can exchange having 26 stones? |
There is a puzzle, which is defined in the title shortly:
> Each of the two spies must pass another one secret numbers (one per spy) unnoticed for enemies. They agreed on a way to do it in advance and today they come to the river, where lies a bunch of 26 identical stones, and to throw stones into the water. First o... |
There is a puzzle, which is defined in the title shortly:
> Each of the two spies must pass another one secret numbers (one per spy) unnoticed for enemies. They agreed on a way to do it in advance and today they come to the river, where lies a bunch of 26 identical stones, and to throw stones into the water. First o... |
You are on your way to visit your Grandma, who lives at the end of the valley. It's her birthday, and you want to give her the cakes you've made.
Between your house and her house, you have to cross 7 bridges, and as it goes in the land of make believe, there is a troll under every bridge! Each troll, quite rightly, ... |
There is a puzzle about two spies:
> Each of the two spies must pass another one secret numbers (one per spy) unnoticed for enemies. They agreed on a way to do it in advance and today they come to the river, where lies a bunch of 26 identical stones, and to throw stones into the water. First one throws a group of st... |
As the question is [currently written](http://puzzling.stackexchange.com/revisions/619/1), there is a trivial answer. While this answer is boring in terms of algebra, it demonstrates the need for careful wording when writing mathematical reasoning. I expect that this is not what is meant, but it's what is written.
>... |
> How do you write 23 using only the number 2?<br /> 34 using only the
> number 3?<br /> 56 using only the number 5?<br /> 100 using only the
> number 9?<br />
You can use only the numbers said, but any math you want in order to get the wanted result
You are allowed to use:
- Fractions
- Addition |
It is really hard to find something about Martin Kruskal relation with origami on the Web.
There is link missed in wikipedia, so may be this information is just a "gossip".
But if you want to see how to fold "envelope for sending secret messages" you can check out:
1. [This][1] method for hard to open envelope.
... |
It is really hard to find something about Martin Kruskal relation with origami on the Web.
There is link missed in wikipedia, so may be this information is just a "gossip".
But if you want to see how to fold "envelope for sending secret messages" you can check out:
1. [This][1] method for hard to open envelope.
... |
There is a puzzle about two spies:
> Each of the two spies must pass another one secret numbers (one per spy) unnoticed for enemies. They agreed on a way to do it in advance and today they come to the river, where lies a bunch of 26 identical stones, and to throw stones into the water. First one throws a group of st... |
In Wikipedia's bibliography of [Martin Kruskal][1] it is said:
> Martin, who had a great love of games, puzzles, and word play of all
> kinds, also invented several quite unusual origami models including an
> envelope for sending secret messages (anyone who unfolded the envelope
> to read the message would have g... |
> Does any user of puzzling.stackexchange have that many arms?
* If your number is 3, the answer will be "no" (unless we have any aliens on the site)
* If your number is 2, the answer will be "yes"
* If your number is 1, the answer will most probably be "maybe". |
There is a puzzle about two spies:
> Two spies must pass each other secret numbers (one per spy) unnoticed for enemies. They agreed on a way to do it in advance and today they come to the river, where lies a bunch of 26 identical stones, and to throw stones into the water. First one throws a group of stones, then se... |
The above answers are correct in a sense, but unfortunately incomplete. There are three scenarios:
**1) The trolls round down.** That is, if you had 3 cakes, they take `floor(1.5) = 1` cake from you. In this case, you may leave home with, at minimum, **zero (0)** cakes.
Why? Consider each troll as below (the ... |
I am looking for hints to find the 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 protection of one soldier. There are other soldiers, but each soldier is at his own house. Houses are ... |
There is a puzzle about two spies:
> Two spies must each pass the other a secret number, unnoticed by their enemies. They have agreed on a method for doing this in advance. They meet at a river, where there is a pile of 26 identical stones. Starting with the first spy, they take turns throwing a group of at least o... |
There is a puzzle about two spies:
> Two spies must pass each other two secret numbers (one number per spy), unnoticed by their enemies. They have agreed on a method for doing this in advance. They meet at a river, where there is a pile of 26 identical stones. Starting with the first spy, they take turns throwing a... |
There is a puzzle about two spies:
> Two spies must pass each other two secret numbers (one number per spy), unnoticed by their enemies. They have agreed on a method for doing this in advance. They meet at a river, where there is a pile of 26 identical stones. Starting with the first spy, they take turns throwing a... |
There are two friends that are not relative, they both have a daughter, and their wives are dead.
each man marries his friend's daughter, and after a while, both couples will have a child(a daughter).
what is the relation of these babies ? |
You are on your way to visit your Grandma, who lives at the end of the valley. It's her birthday, and you want to give her the cakes you've made.
Between your house and her house, you have to cross 7 bridges, and as it goes in the land of make believe, there is a troll under every bridge! Each troll, quite rightly, ... |
There is a puzzle about two spies:
> Two spies must pass each other two secret numbers (one number per spy), unnoticed by their enemies. They have agreed on a method for doing this in advance. They meet at a river, where there is a pile of 26 identical stones. Starting with the first spy, they take turns throwing a... |
There is a puzzle about two spies:
> Two spies must pass each other two secret numbers (one number per spy), unnoticed by their enemies. They have agreed on a method for doing this in advance. They meet at a river, where there is a pile of 26 identical stones. Starting with the first spy, they take turns throwing a... |
There is a puzzle about two spies:
> Two spies must pass each other two secret numbers (one number per spy), unnoticed by their enemies. They have agreed on a method for doing this using only 26 indistinguishable stones in advance. They meet at a river, where there is a pile of 26 stones. Starting with the first spy... |
There is a puzzle about two spies:
> Two spies must pass each other two secret numbers (one number per spy), unnoticed by their enemies. They have agreed on a method for doing this using only 26 indistinguishable stones in advance. They meet at a river, where there is a pile of 26 stones. Starting with the first spy... |
There is a puzzle about two spies:
> Two spies must pass each other two secret numbers (one number per spy), unnoticed by their enemies. They have agreed on a method for doing this using only 26 indistinguishable stones in advance. They meet at a river, where there is a pile of 26 stones. Starting with the first spy... |
There is a puzzle about two spies:
> Two spies must pass each other two secret numbers (one number per spy), unnoticed by their enemies. They have agreed on a method for doing this using only 26 indistinguishable stones in advance. They meet at a river, where there is a pile of 26 stones. Starting with the first spy... |
You are on your way to visit your Grandma, who lives at the end of the valley. It's her birthday, and you want to give her the cakes you've made.
Between your house and her house, you have to cross 7 bridges, and as it goes in the land of make believe, there is a troll under every bridge! Each troll, quite rightly, ... |
The Octo-Star was originally created by David Pitcher, who called it the OctoCube, and released it in January 2013. It was subsequently mass-produced by Calvin Puzzles in January 2014.
The original video from its creator is available [here](https://www.youtube.com/watch?v=xFN73NH5OBk), showcasing the original Shapew... |
>A lighthouse keeper decides to take a bath an hour before the next lighthouse keeper comes to relieve him of his shift.
>This lighthouse keeper is having a bad day. First he looks himself in the bathroom, he's not going to be able to get out until the next lighthouse keeper arrives and is able to unlock the bathro... |
There are two friends, they are not related. Each has a daughter. Their wives are dead.
Each man marries his friend's daughter, and after a while, both couples will have a child (a daughter).
What is the relationship between the two babies? |
There is a puzzle
> Suppose a standard 8x8 chessboard has two unknown (any) cells removed. The only thing is knows that cells had *different* colours. Is it always possible to place 31 dominoes of size 2x1 so as to cover all of these squares?
The answer is
>! yes
and there is very clever and fast prove.
I... |
Is there brute-force solution of Chessboard and dominoes puzzle? |
There is a puzzle
> Suppose a standard 8x8 chessboard has two unknown (any) cells removed. The only thing is knows that cells had *different* colours. Is it always possible to place 31 dominoes of size 2x1 so as to cover all of these squares?
The answer is
>! yes
and there is very clever and fast prove:
>... |
Is there a brute-force solution of this puzzle? |
There is well known task:
> How to divide a pie between two people, so each will think that he got equal or more that the other one?
It has the following solution:
>! First person divide the pie on 2 equal (in his opinion) parts. Second one choses the biggest one.
Is it possible to generalise this on N peop... |
How to generalise Partition of the pie puzzle? |
You are in the intersection of two roads,
there is a troll in the beginning of each road.
One of them is liar (***always*** lies), and one of them ***always*** tells the truth.
One of the roads, ends to your destination and one of them ends to **death** :) .
The trolls know which way is the right one and w... |
The idea is to ask question about question. In that case lie+lie=truth, truth+truth=truth.
An example of such a question is:
**What would you tell me if I ask you whether this road ends to death?**
If answer is "yes" you better do not take this road. |
The idea is to ask question about question. In that case `lie+lie = truth+truth = truth` (or `lie+truth = truth+lie = lie`).
An example of such a question is:
**What would you tell me if I ask you whether this road ends to death?**
If answer is "yes" you better do not take this road. |
Here is the solution I found. Please tell, if you see any mistakes.
Let's call \$M'\$ maximum number of jokers, which can be among group of chosen \$N'\$ man according to our knowledge.
Our start group will include all men, \$N' = N\$. Our knowledge is that \$K+M=N, K>M\$, therefore \$M'= (N-1)/2\$.
The goal ... |
There is well known task:
> How to divide a pie between two people, so each will think that he got equal or more that the other one?
It has the following solution:
>! First person divide the pie on 2 equal (in his opinion) parts. Second one choses the biggest one.
Is it possible to generalise this on N envy... |
There is well known task:
> How to divide a pie between two people, so each will think that he got equal or more that the other one?
It has the following solution:
>! First person divide the pie on 2 equal (in his opinion) parts. Second one choses the biggest one.
I know that it is possible to generalise in... |
How to generalise Partition of the pie for N envy people? |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.