instruction stringlengths 15 30k |
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I would repeat here a big part of answer on similar, but not identical question: http://puzzling.stackexchange.com/a/1666/28 . It solves this problem in **98 questions** at most, and in 50 questions if we are lucky.
Let's call $M$ maximum number of faulty, which can be among group of chosen $N$ computers according t... |
I would repeat here a big part of answer on similar, but not identical question: http://puzzling.stackexchange.com/a/1666/28 . This algorithm guarantee to find one working computer in **97 questions**, and if we are lucky it will need only 49 questions.
Let's call $M$ maximum number of faulty, which can be among gro... |
I would repeat here a big part of answer on similar, but not identical question: http://puzzling.stackexchange.com/a/1666/28 . This algorithm guarantee to find one working computer in **97 questions**, and if we are lucky it will need only 49 questions.
Let's call $M$ maximum number of faulty, which can be among gro... |
I would repeat here a big part of answer on similar, but not identical question: http://puzzling.stackexchange.com/a/1666/28 . This algorithm guarantee to find one working computer in **97 questions**, and if we are lucky it will need only 49 questions.
Let's call $M$ maximum number of faulty, which can be among gro... |
I would repeat here a big part of answer on similar, but not identical question: http://puzzling.stackexchange.com/a/1666/28 . This algorithm guarantee to find one working computer in **97 questions**, and if we are lucky it will need only 49 questions.
Let's call $M$ maximum number of faulty, which can be among Gro... |
Standard knights and knaves problem. There are 10 people in a room, you know that each person will either always tell the truth or always lie, but you don't know who is a truth teller or liar.
You are in a room with 5 doors. Four of the doors lead to horrible hazards like an endless pit, a fiery inferno, or bein... |
The one who made it didn't want it
The one who bought it didn't need it
The one who received it didn't wish for it.
The one who used it never saw it
What is it? |
I suppose you allowed to ask only yes-or-no questions.
In this case 2 questions allows you to chose only between 2x2=4 options, so you need at least 3 questions.
It is very easy to formulate them. Just ask each time "What would you answer if I ask you blabla" and you will know the truth about blabla. Let's use ... |
A) In this case I suppose you are allowed to ask only yes-or-no questions.
In this case 2 questions allows you to chose only between 2x2=4 options, so you need at least 3 questions.
It is very easy to formulate them. Just ask each time "What would you answer if I ask you blabla" and you will know the truth about ... |
- The one who made it didn't want it
- The one who bought it didn't need it
- The one who received it didn't wish for it
- The one who used it never saw it
What is it? |
Standard knights and knaves problem. There are 10 people in a room, you know that each person will either always tell the truth or always lie, but you don't know who is a truth teller or liar.
You are in a room with 5 doors. Four of the doors lead to horrible hazards like an endless pit, a fiery inferno, or bein... |
You have a stack of cards numbered from 1 to N in random order.
You want to sort the cards in ascending order using the following procedure:
1. Your initial stack is stack 1.
2. You distribute the cards from stack 1 to stack 2 and 3: you take the topmost card on stack 1, put it on top of stack 2 or stack 3, and ... |
You have a stack of N cards numbered from 1 to N in random order.
You want to sort the cards in ascending order using the following procedure:
1. Your initial stack is stack 1.
2. You distribute the cards from stack 1 to stack 2 and 3: you take the topmost card on stack 1, put it on top of stack 2 or stack 3, an... |
You have a stack of N cards numbered from 1 to N in random order.
You want to sort the cards in ascending order using the following procedure:
1. Your initial stack is stack 1.
2. You distribute the cards from stack 1 to stack 2 and 3: you take the topmost card on stack 1, put it on top of stack 2 or stack 3, an... |
- The one who made it didn't want it
- The one who bought it didn't need it
- The one who received it didn't wish for it
- The one who used it never saw it
What is it? |
You have a stack of N cards numbered from 1 to N in random order.
You want to sort the cards in ascending order using the following procedure:
1. Your initial stack is stack 1.
2. You distribute the cards from stack 1 to stack 2 and 3: you take the topmost card on stack 1, put it on top of stack 2 or stack 3, an... |
If I asked your twin which gender you are, what would they tell me?
Even if they're both liars you'll get the right answer - as the one you're asking would lie about what the other would say, who would also lie.
---
For the people confused about this, in the world of riddles the person you're asking is an orac... |
You should see a standard chessboard - it is printed on paper. How many ways can you cut it up (around the squares) such that each piece has twice as much squares of one colour than of the other colour?
![Chessboard][1]
[1]: https://i.stack.imgur.com/ks8ho.png |
Similarly to this question: [How many Queens to threaten themselves][1].
What it the maximum number of queens you can place on an 8*8 board such that each queen is attacked precisely twice:
1) with no other pieces on the board?
2) other pieces are allowed?
I thought this was a legitimately interesting varia... |
Similarly to this question: [How many Queens to threaten themselves][1].
What it the maximum number of queens you can place on an 8*8 board such that each queen is attacked precisely twice:
1. with no other pieces on the board?
2. other pieces are allowed?
I thought this was a legitimately interesting varia... |
Eh? A piece that has $k$ squares of one color and $2k$ squares of the other color has $3k$ squares. It is a multiple of $3$. You cannot split $64$ squares in two parts that boh have a multiple of $3$ squares.
So the answer is: there is no way. |
You are given 4 balls, all equal in weight except for one that is either heavier or lighter. You are also given a two-pan balance to use. In each use of the balance you may put any number of the 4 balls on the left pan, and the same number on the right pan, and push a button to initiate the weighing; there are three po... |
As [remarked by sth](http://puzzling.stackexchange.com/questions/2693/a-blanket-for-my-baby-snake/2711#comment6357_2693), this is an open problem, a topic of ongoing research. It is known as [Moser's worm problem](http://en.wikipedia.org/wiki/Moser%27s_worm_problem). The [Math Overflow](http://mathoverflow.net/) thread... |
If I asked your twin which gender you are, what would they tell me?
Even if they're both liars you'll get the right answer - as the one you're asking would lie about what the other would say, who would also lie.
---
For the people confused about this, in the world of riddles the person you're asking is an orac... |
The little old man has twelve children: some short, some long, some cold, some hot.
Who is he? |
Who is this old man? |
Warning: To answer this riddle you need to have a through all understanding of how time works.
Two twins were born during the same year, on the same month, and the same day, 10 min. apart. By the time twin A was 100, twin B was younger by more than 10 minutes, fairly slightly. Neither twin died during the 100 years.... |
Warning: To answer this riddle you need to have a through all understanding of how time works.
> Two twins were born during the same year, on the same month, and the same day, 10 minutes apart. By the time twin A was 100, twin B was younger by more than 10 minutes, fairly slightly. Neither twin died during the 100 y... |
Queen is a mix of Bishop and Rock. Let's create a chess piece that is a mix of regular queen and knight. Name it Super-Queen.
The question is how many of these Super-Queens can place on a standard chessboard that non of them attack each other without any other piece?
**Hint:**
>! It's obvious that it should be ... |
How many Super-Queens? |
You have a stack of N cards numbered from 1 to N in random order.
You want to sort the cards in ascending order using the following procedure:
1. Your initial stack is stack 1.
2. You distribute the cards from stack 1 to stack 2 and 3: you take the topmost card on stack 1, put it on top of stack 2 or stack 3, an... |
Queen is combination of Bishop and Rook and [Amazon][1] is combination of queen and knight.
The question is how many Amazons can place on a standard chessboard that non of them attack each other without any other pieces allowed?
**Hint:**
>! It's obvious that it should be a smaller number than 9. Also 8 is impo... |
How many Amazons on chessboard? |
The solution to the restricted version still works, but it is no longer unique. I'll give a proof that the previous solution still works. According to [Joe Z.'s answer][1], Summer is given $x+y=17$, and Proctor is given $x \cdot y=52$. Also, to avoid confusion I'm going to call Proctor male and Summer female.
Becaus... |
How many knights can you fit on a chess board without either being attacked? |
How Many Knights on a Chess Board? |
How many squares can you control with only one set of chess pieces of the same color? (8 Pawns, 2 Knights, 2 Bishops, 2 Rook, Queen and King) |
How many squares can standard chess pieces control? |
How many squares can you control with only one set of chess pieces of the same color? (8 Pawns, 2 Knights, 2 Bishops, 2 Rook, Queen and King)
Edit: Pieces cannot attack (control) the square they are currently occupied. |
Is it possible to order a complete set of chess pieces of the same color (8 Pawns, 2 Knights, 2 Bishops, 2 Rook, Queen and King) in a way that non of them attack each other? How? |
How Many Speedy Knights on a Chess Board? |
How many Chess Pieces are needed to control every square on the board? |
Pirates have buried treasure on a very unusual perfectly circular desert island, with no trees or obstacles of any kind. The map takes me to the island but doesn't tell me where to find it on the island.
It only tells me that it's buried under a small x marked on the ground.
The tide is coming in fast so I have ... |
Pirates have buried treasure on a very unusual perfectly circular desert island, with no trees or obstacles of any kind. The map takes me to the island but doesn't tell me where to find it on the island.
It only tells me that it's buried under a small x marked on the ground.
The tide is coming in fast so I have ... |
Let's continue the induction, since the jump to 99 blue eyes does seem weird. After all, every one knows that someone has blue eyes.
If there are 4 blue eyed-people, A will look at B,C,D, thinking :
> May be I don't have blue eyes (only 3 blue eyes?). In this case B must be thinking, that he may not have blue eye... |
You accepted an answer, but it doesnt answer the question you asked: Who is the old man? Its Father Time. |
Is the answer 12 mm? He says nothing about having all the volumes, just that he arranged volume 1 and 32.
Building on the most upvoted answer, the first page of volume one sits on the right having only volume 1's cover separating it from volume 32 cover, that has its final page sitting on the left side of the book.
... |
How many pieces can you organize on a Chess board without one side being attacked by the other? This scoring will be used to prove you have the highest.
**Piece cost:**
* Pawn - 1
* Knight - 3
* Bishop - 3
* Rook - 5
* Queen - 9
**Rules:**
* Both sides must have the same pieces on the board
* Your sc... |
How Many Pieces from Both Sides can you Place on a Chess Board Without Attacking a Side? |
I was helping Ernie clean out his shed a while back when I saw a curious old machine. "Oh yeah, that!" said Ernie, when I pointed it out to him. "A few years back, before transistors were invented, I tried to make a clockwork calculator. It worked, but was never a commercial success." The machine consisted two rows of ... |
I was helping Ernie clean out his shed a while back when I saw a curious old machine. "Oh yeah, that!" said Ernie, when I pointed it out to him. "A few years back, before transistors were invented, I tried to make a clockwork calculator. It worked, but was never a commercial success." The machine consisted two rows of ... |
Ok, so my friends and I had a disagreement over this seemingly simple problem and we would very much like to know the answer for it.
Question: "Initially a 20 kg watermelon is 96pc water and 4pc pulp. After keeping it out in the sun for (say X) hours, the watermelon is now 95pc water. What is the weight of the wat... |
Ok, so my friends and I had a disagreement over this seemingly simple problem and we would very much like to know the answer for it.
Question: "Initially a 100 kgs watermelon is 96pc water and 4pc pulp. After keeping it out in the sun for (say X) hours, the watermelon is now 95pc water. What is the weight of the wat... |
A wealthy person has passed away, naming three siblings as beneficiaries of the vast estate. Unfortunately, the will states that:
> My estate shall be divided evenly, such that no sibling shall feel their share is smaller than any other share.
As the estate contains many illiquid assets of sentimental value, one ... |
You may use as many pieces as you like. Pieces do not control the square they occupy.
Accepted Answer goes to the person that has the least score.
Piece cost:
Pawn - 1
Knight - 3
Bishop - 3
Rook - 5
Queen - 9
**Note1**: The king has no score, it was implied that it is not allowed.
**Note2**: I meant ... |
How many Chess Pieces are needed to control every square on the board? No Piece Restriction |
You may use as many pieces as you like. Pieces do not control the square they occupy.
Accepted Answer goes to the person that has the least score.
Piece cost:
- Pawn - 1
- Knight - 3
- Bishop - 3
- Rook - 5
- Queen - 9
**Note1**: The king has no score, it was implied that it is not allowed.
**Note2**... |
Ok, so my friends and I had a disagreement over this seemingly simple problem and we would very much like to know the answer for it.
> ### Question ###
> Initially a 100 kgs watermelon is 96pc water and 4pc pulp. After keeping it out in the sun for (say X) hours, the watermelon is now 95pc water. What is the weight... |
I have a complete set of encyclopaedias on my bookshelf, beautifully bound and neatly arranged with volume 1 on the left and volume 32 on the right. They were a talking point when I bought them 30-odd years ago and were regularly used, but as the internet took off so my use of them declined, preferring to use the onlin... |
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 the thought that he had 365 days running for him, the second hustler was pleased to accept. Suspecting, not unnatura... |
You have a stack of N cards numbered from 1 to N in random order.
You want to sort the cards in ascending order using the following procedure:
1. Your initial stack is stack 1.
2. You distribute the cards from stack 1 to stack 2 and 3: you take the topmost card on stack 1, put it on top of stack 2 or stack 3, an... |
You have a stack of N cards numbered from 1 to N in random order.
You want to sort the cards in ascending order using the following procedure:
1. Your initial stack is stack 1.
2. You distribute the cards from stack 1 to stack 2 and 3: you take the topmost card on stack 1, put it on top of stack 2 or stack 3, an... |
You have a stack of N cards numbered from 1 to N in random order.
You want to sort the cards in ascending order using the following procedure:
1. Your initial stack is stack 1.
2. You distribute the cards from stack 1 to stack 2 and 3: you take the topmost card on stack 1, put it on top of stack 2 or stack 3, an... |
The **Bunny** is the new and improved Pawn (It's a Chess piece) it moves just like the pawn, but can move in all directions, diagonally, 1 tile. It can move up 2 spaces forwards, to reach a different coloured tile by Bunny-Hoping over another Bunny, to 2 spaces ahead of him. How can you alternate moves (move **Bunny 1*... |
Warning: To answer this riddle you need to have a through all understanding of how time works.
> Two twins were born during the same year, on the same month, and the same day, exactly 10 minutes apart. By the time twin A was 100, twin B was younger by more than 10 minutes, fairly slightly. Neither twin died during t... |
I was helping Ernie clean out his shed a while back when I saw a curious old machine. "Oh yeah, that!" said Ernie, when I pointed it out to him. "A few years back, before transistors were invented, I tried to make a clockwork calculator. It worked, but was never a commercial success." The machine consisted two rows of ... |
How many knights can you fit on a chess board without any being threatened? |
The maximal number of knights of a single color that can be placed on a chessboard without any knight being one knights-move away from any other is 32; such a position may easily be achieved by placing all 32 knights on squares of the same color.
If one uses both black pieces and white pieces, it's possible to place... |
I was helping Ernie clean out his shed a while back when I saw a curious old machine. "Oh yeah, that!" said Ernie, when I pointed it out to him. "A few years back, before transistors were invented, I tried to make a clockwork calculator. It worked, but was never a commercial success." The machine consisted two rows of ... |
The **Bunny** is the new and improved Pawn (It's a Chess piece) it moves just like the pawn, but can move in all directions, diagonally, 1 tile. It can move up 2 spaces forwards, to reach a different coloured tile by Bunny-Hoping over another Bunny, to 2 spaces ahead of him. How can you alternate moves (move **Bunny 1*... |
Heaven has a countably infinite number of cloud for people to stay, each of which has a good soul living on it.
A countably infinite number of infinite universes are extinguished by God (their beta period had expired). So, a countably infinite number of groups of good souls (each of which are countably infinite in... |
How will God accommodate these people? |
The **Bunny** is the new and improved Pawn (It's a Chess piece) it moves just like the pawn, but can move in all directions, diagonally, 1 tile. It can move up 2 spaces forwards, to reach a different coloured tile by Bunny-Hoping over another Bunny, to 2 spaces ahead of him. How can you alternate moves (move **Bunny 1*... |
Heaven has a countably infinite number of cloud for people to stay, each of which has a good soul living on it.
A countably infinite number of infinite universes are extinguished by God (their beta period had expired). So, a countably infinite number of groups of good souls (each of which are countably infinite in s... |
The **Bunny** is the new and improved Pawn (It's a Chess piece) it moves just like the pawn **captures**, but can move in all directions, diagonally, 1 tile. It can move up 2 spaces forwards, to reach a different coloured tile by Bunny-Hoping over another Bunny, to 2 spaces ahead of him. How can you alternate moves (mo... |
This does not qualify as the lowest score, but it does answer the question of
> How many Chess Pieces are needed to control every square on the board?
![enter image description here][1]
[1]: https://i.stack.imgur.com/luPqp.png
It takes 5 pieces |
You have a stack of N cards numbered from 1 to N in random order.
You want to sort the cards in ascending order using the following procedure:
1. Your initial stack is stack 1.
2. You distribute the cards from stack 1 to stack 2 and 3: you take the topmost card on stack 1, put it on top of stack 2 or stack 3, an... |
The **Bunny** is a new chess piece. Like a bishop, it only moves diagonally (in any of the 4 directions). Like a king, it only moves by one tile at a time. Additionally, the bunny can make a different move. It can move up **2 spaces forwards**, to reach a different coloured tile by *bunny-hopping* over another Bunny, t... |
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 ... |
You have a stack of N cards numbered from 1 to N in random order.
You want to sort the cards in ascending order using the following procedure:
1. Your initial stack is stack 1.
2. You distribute the cards from stack 1 to stack 2 and 3: you take the topmost card on stack 1, put it on top of stack 2 or stack 3, an... |
For the following pattern of filling the $5*5$ matrix, how many steps does it take to turn all cells of the matrix to black?
![enter image description here][1]
Pattern has revealed by [eBusiness][2]:
>! The first piece moves to the right, the second moves down, the third moves left, the fourth moves up, and so... |
When will the matrix turn to black? |
The **Bunny** is a new chess piece. Like a bishop, it only moves diagonally (in any of the 4 directions). Like a king, it only moves by one tile at a time. Additionally, the bunny can make a different move. It can move **2 spaces forwards**, (by forward I mean over the bunny, which can be in any direction), to reach a ... |
You have a stack of N cards numbered from 1 to N in random order.
You want to sort the cards in ascending order using the following procedure:
1. Your initial stack is stack 1.
2. You distribute the cards from stack 1 to stack 2 and 3: you take the topmost card on stack 1, put it on top of stack 2 or stack 3, an... |
![Solution?][1]
I wanted to try to make use of the kings, and this is what I got. It ends up at a score of 23.
[1]: https://i.stack.imgur.com/OXgSx.gif |
Let's say there's 5x5 grid and starting position is upper left corner, and ending position is lower left corner. How to count how many paths there are?
I know the answer is 86. But how? (4x5 is 8, 3x3 is 2)
I need to learn calculate larger grids. |
How to count Hamiltonian paths of grid? |
Let's say there is a 5x5 grid with a starting position in the upper left corner, and an ending position is lower left corner. How do I count how many paths there are through the grid?
I know the answer is 86 for a 5x5 grid. But how should I calculate this? (4x5 is 8, 3x3 is 2) I want to learn calculate larger grids... |
How do I count Hamiltonian paths of grid? |
I made up this puzzle, so if you are only keen on answering standard puzzles, I am sorry, I thought its been a dull day for questions so I made up my own
Here is a 7 x 7 squares image with 7 8 letter English words hidden in it can you find the words?
![enter image description here][1]
[1]: https://i.stack.... |
Let's say there is a 5x5 grid with a starting position in the upper left corner, and an ending position is lower left corner. How do I count how many Hamiltonian paths there are through the grid?
I know the answer is 86 for a 5x5 grid. But how should I calculate this? (4x4 is 8, 3x3 is 2) I want to learn calculate ... |
The [Numberplay][1] blog on the NY Times website used to have word ladder puzzles along with their weekly math puzzles. I found them fun and so I figured I'd introduce them here. These aren't just your basic word ladders either.
1. You can change a single letter in place, as in traditional word ladders — for examp... |
Two girls went to dinner together and both ordered iced tea. One girl pounded down five of them in the time it took the other to drink one. The girl who drank one died, while the girl who drank five survived. All of the drinks were poisoned.
Why did the girl that drank more iced tea survive? |
An old farmer passes away in his sleep. After a suitable period of mourning, his three sons find their father's will in his study.
Amongst other, simpler bequests is the following:
"I wish my small flock of sheep to be well cared for, with the responsibility split between my three suns. Therefore take the pack of car... |
An old farmer passes away in his sleep. After a suitable period of mourning, his three sons find their father's will in his study.
Amongst other, simpler bequests is the following:
"I wish my small flock of sheep to be well cared for, with the responsibility split between my three suns. Therefore take the pack of car... |
Is it possible to setup a chess board where every square on the board is only controlled once. Occupying a square does not mean controlling it.
If it is possible, with how little pieces?
**Piece Cost:**
* Pawn: 1
* Bishop: 3
* Knight: 3
* Rook: 5
* Queen: 9
You are not allowed to use the king. |
Using only the one colour set; Is it possible to setup a chess board where every square on the board is only controlled once. Occupying a square does not mean controlling it.
If it is possible, with how little pieces?
**Piece Cost:**
* Pawn: 1
* Bishop: 3
* Knight: 3
* Rook: 5
* Queen: 9
**You... |
This is the problem i came across reading the book "The art and craft of problem solving". I read this question I couldn't able to figure out the solution and I saw the solution after a while, but still I couldn't able to understand the solution as well.
Question:
Pat wants to take a I .5-meter-long sword onto a ... |
This is the problem I came across reading the book "The art and craft of problem solving". I read this question I couldn't able to figure out the solution and I saw the solution after a while, but still I couldn't able to understand the solution as well.
Question:
Pat wants to take a $1.5$-meter-long sword onto a... |
This is the problem I came across reading the book "The art and craft of problem solving". I read this question I couldn't able to figure out the solution and I saw the solution after a while, but still I couldn't able to understand the solution as well.
Question:
Pat wants to take a $1.5$-meter-long sword onto a... |
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