instruction stringlengths 15 30k |
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On one of the Islands of Knights and Knaves you land for the purposes of an anthropological survey. The Island has Knights who always tell the truth ( if they know enough information regarding a question put to them) and Knaves who always lie ( also if they know enough relevent info.) ( Of course a Knight or Knave cou... |
A bridge goes over a river and you ford a river? |
From the formulation I would conclude that a tax-collector can answer whatever he finds reasonable, using any unknown algorithm to generate answer. This includes random generator algorithms for question which are asked a first time (next time he will repeat the answer).
In this case it is quite obvious that the answ... |
*From the formulation I would conclude that a tax-collector can answer whatever he finds reasonable, using any unknown algorithm to generate answer. This includes random generator algorithms for question which are asked a first time (next time he will repeat the answer).*
In this case it is quite obvious that the ... |
As noted in Jason's answer, both *bridge* and *ford* have to do with rivers, in these cases the [Cam](http://en.wikipedia.org/wiki/River_Cam) and the [Isis](http://en.wikipedia.org/wiki/The_Isis) portion of the [Thames](http://en.wikipedia.org/wiki/River_Thames).
Etymonline's *[Cambridge](http://www.etymonline.com/i... |
**Intuitive Answer**
Assuming "sometimes lies and sometimes tells the truth" means that a tax collector will lie for at least one question and tell the truth for at least one question, then we can have the following two tax collector collections:
- Tax collectors of type #1 will give the same answer a Knight give... |
The task is to decode the following: 5, 18, 92, 6, 1
Clues:
1. It's your name [my name is Jake]
2. Gliding o'er all, through all, Through Nature, Time, and Space, As a ship on the waters advancing, The voyage of the soul—not life alone, Death, many deaths I'll sing.
3. Your first guess (ASCII) was definitely t... |
Lately I found different versions of this puzzle, I was wondering if it has a name or belongs to a specific kind, so that I can understand more.
Here it is:
> Peter got 10 from his father, 10 from his mother and went to buy some
> grocery. He spent only 17.
>
> Once he is back home he gives back 1 to his father... |
The [unexpected hanging paradox][1] is as follows:
> A judge tells a condemned prisoner that he will be hanged at noon on
> one weekday in the following week but that the execution will be a
> surprise to the prisoner. He will not know the day of the hanging
> until the executioner knocks on his cell door at noon... |
The simple and I believe the only answer to both your question is "This is paradox, so logic does not have predictability power here".
Marting Gardner described this paradox in details. Unfortunately I can't find english version online, but if you know russian you can find it [here][1]. English version should be in ... |
The simple and I believe the only answer to both your question is "This is paradox, so logic does not have predictability power here".
Marting Gardner described this paradox in details. Unfortunately I can't find english version online, but if you know russian you can find it [here][1] (english google translation is... |
Where is that last dollar gone? |
Where has the last dollar gone? |
A woman works at a ball factory. She's instructed to open up a ball creation kit composed of one red rubber ball and two strips of digit stickers from $0$ through $9$.
She's instructed to do the following:
1. Starting with $1$, write the current number on the ball using the digits available on the 2 strips.
2.... |
**The simple and I believe the only answer to both your question is "This is paradox, so logic does not have predictability power here".**
Marting Gardner described this paradox in details. Unfortunately I can't find english version online, but if you know russian you can find it [here][1] (english google translatio... |
Let's lay down some groundwork to help us out:
- Let $req(n, d)$ be the number of digit $d$ required to write out all the numbers from 1 to $n$.
- Since each kit contains two of each digit, we have $2n$ of each digit
- This means we want the smallest $n$ for which $req(n, d) > 2n$ for some $d$
It seems like ... |
Let's lay down some groundwork to help us out:
- Let $req(n, d)$ be the number of digit $d$ required to write out all the numbers from 1 to $n$.
- Since each kit contains two of each digit, we have $2n$ of each digit
- This means we want the smallest $n$ for which $req(n, d) > 2n$ for some $d$
It seems like ... |
Last year, just before my birthday in February, I noticed something unsual about my age. The last two digits of my birth year were the same as my age. How old was I then and was this an unusual occurance? |
Last year, just before my birthday in February, I noticed something unsual. The last two digits of my birth year were the same as my age. How old was I then and was this an unusual occurance? |
Let's lay down some groundwork to help us out:
- Let $req(n, d)$ be the number of digit $d$ required to write out all the numbers from 1 to $n$.
- Since each kit contains two of each digit, we have $2n$ of each digit
- This means we want the smallest $n$ for which $req(n, d) > 2n$ for some $d$
It seems like ... |
Bruce found a nice quote on web, then wrote it in on a square piece of paper and leave it some where on his room. The quote had exactly 64 characters excluding spaces. He has written the characters in 8 rows and 8 columns, ignoring word-breaking.
His younger sister Kim was helping Bruce to clean his room and thought... |
Bruce found a nice quote on web, then wrote it in on a square piece of paper and leave it some where on his room. The quote had exactly 64 characters excluding spaces. He has written the characters in 8 rows and 8 columns, ignoring word-breaking.
His younger sister Kim was helping Bruce to clean his room and imagine... |
I've tried to explain the solution using as little math as possible, and to give some intuition as to what makes it tick. Nonetheless there will be a little mathematical notation at the end.
### First steps: going beyond the obvious solution in the simplest case (N=2)
The statement of the puzzle as presented here... |
I've tried to explain the solution using as little math as possible, and to give some intuition as to what makes it tick. Nonetheless there will be a little mathematical notation at the end.
### First steps: going beyond the obvious solution in the simplest case (N=2)
The statement of the puzzle as presented here... |
As noted before, the first digit to run out will be the 1's.
If you consider the units you use, you'll see that you use 1,2,3,...,9,0 and restart. At any time you'll have used more 1's than any other number. If you connsider the tens, you see that you use 10x1, 10x2, ..., 10x9, 10x0. Again you'll use up 1's befor... |
As noted before, the first digit to run out will be the 1's.
If you consider the units you use, you'll see that you use 1,2,3,...,9,0 and restart. At any time you'll have used the 1 before any other number. If you consider the tens, you see that you use 10x1, 10x2, ..., 10x9, 10x0. Again you'll use 1's before the... |
As noted before, the first digit to run out will be the 1's.
If you consider the units you use, you'll see that you use 1,2,3,...,9,0 and restart. At any time you'll have used the 1 before any other number. If you consider the tens, you see that you use 10x1, 10x2, ..., 10x9, 10x0. Again you'll use 1's before the... |
Let's lay down some groundwork to help us out:
- Let $req(n, d)$ be the number of digit $d$ required to write out all the numbers from 1 to $n$.
- Since each kit contains two of each digit, we have $2n$ of each digit
- This means we want the smallest $n$ for which $req(n, d) > 2n$ for some $d$
It seems like ... |
Let's lay down some groundwork to help us out:
- Let $req(n, d)$ be the number of digit $d$ required to write out all the numbers from 1 to $n$.
- Since each kit contains two of each digit, we have $2n$ of each digit
- This means we want the smallest $n$ for which $req(n, d) > 2n$ for some $d$
It seems like ... |
This being Halloween we will consider the problem of witches and their cats. The whole crowd is out tonight, naturally. And an interested observer, seeing them fly by, yes witches cats fly, noticed that the number of legs all told was 5 times the number of heads and the total heads and legs was 72. How many cats and wi... |
Bruce found a nice quote on the web, then wrote it in on a square piece of paper and left it somewhere in his room. The quote had exactly 64 characters excluding spaces. He has written the characters in 8 rows and 8 columns, ignoring word-breaking.
His younger sister Kim was helping Bruce to clean his room and thoug... |
On an Island of Knight and Knaves a Knight will never contradict himself unless some true facts about something changes. I was wondering could a Knave contradict himself ( regarding presently unchanging facts)? If he did wouldn't that mean he told the truth about 'something'? |
Knave can easily contradict himself.
For example, let's take a set of facts:
A is FALSE
B is TRUE
If you ask a knave "what is A?" he will answer TRUE. Then "what is B?" - he will answer FALSE.
Then ask what A AND B is. He will answer TRUE (FALSE AND TRUE = FALSE).
But cobmining his previous answers lo... |
Knave can easily contradict himself.
For example, let's take a set of facts:
Fact A, which is FALSE
Fact B, which is TRUE
If you ask a knave "what is A?" he would answer TRUE. Then "what is B?" - he would answer FALSE.
Then ask what A AND B is. He would answer TRUE (FALSE AND TRUE = FALSE).
But cobmin... |
Knave can easily contradict himself.
For example, let's take a set of facts:
Fact A, which is FALSE
Fact B, which is TRUE
If you ask a knave "what is A?" he would answer TRUE. Then "what is B?" - he would answer FALSE.
Then ask what A AND B is. He would answer TRUE (FALSE AND TRUE = FALSE).
But cobmin... |
A knave can contradict himself easily.
\- Is the sky blue?
\- No.
\- Did you just answer no?
\- No.
|
It's a simple pattern I thought of. Here it is:
1,1,1,3,3,6,6,10,10,22,22,44,44,84,?,?,?,?,?
Whoever gives the correct answer and a good explaination gets upvote and best answer. |
When Cora was killed, Anna and Beth were questioned by the police about the manner of her death by poison.
Anna: If it was a murder, Beth did it.
Beth: If it was not suicide, it was murder.
The policemen made the following assumptions:
1. If neither Anna nor Beth lied, it was an accident.
2. If either Anna or Beth... |
Accident/Suicide because of contradictive facts?
If it was not an accident, it was murder.
If that's a lie it was murder.
I'm lost... |
Accident/Suicide because of contradictive facts?
If it was not an accident, it was murder.
If that's a lie it was murder.
So if it was an accident it was murder...
Accidental murder? XD |
So, recently there was a very good riddle posted here: http://puzzling.stackexchange.com/questions/626/paying-the-troll-toll. I would like to propose a similar question which might have been partially answered. But anyways...
So, same basic idea as the original Paying the Troll toll riddle, however, assume now that ... |
Start with S(1) = 1.
To construct the next 6 numbers (S(2) - S(7)), use n = 1 and apply the following formulas:
S(2) = S(1) * 2 + (-1)*n
S(3) = S(2)
S(4) = S(3) * 2 + (+1)*n
S(5) = S(4)
S(6) = S(5) * 2 + ( 0)*n
S(7) = S(6)
To construct the next 6 numbers, double n to 2 and apply ... |
Miss Danner, a primary school teacher, is on her way to school - it's the first day of school this year.
In class, she sees two identically looking boys sitting in the first row.
>Aw, twins, so cute!
she exclaims.
>We aren't twins.
the boys respond unisono.
Miss Danner - astounded - doesn't comment it... |
Miss Danner, a primary school teacher, is on her way to school - it's the first day of school this year.
In class, she sees two identically looking boys sitting in the first row.
>Aw, twins, so cute!
she exclaims.
>We aren't twins.
the boys respond unisono.
Miss Danner - astounded - doesn't comment it... |
So, recently there was a very good riddle posted here: http://puzzling.stackexchange.com/questions/626/paying-the-troll-toll. I would like to propose a similar question which might have been partially answered. But anyways...
So, same basic idea as the original Paying the Troll toll riddle, however, assume now that ... |
It's a simple pattern I thought of. Here it is:
1,1,1,3,3,6,6,10,10,22,22,44,44,84,?,?,?,?,?
Whoever gives the correct answer and a good explaination gets best answer. |
Miss Danner, a primary school teacher, is on her way to school - it's the first day of school this year.
In class, she sees two identically looking boys sitting in the first row.
>Aw, twins, so cute!
she exclaims.
>We aren't twins.
the boys respond unisono.
Miss Danner - astounded - doesn't comment it... |
Miss Danner, a primary school teacher, is on her way to school - it's the first day of school this year.
In class, she sees two identically looking boys sitting in the first row.
>Aw, twins, so cute!
she exclaims.
>We aren't twins.
the boys respond unisono.
Miss Danner - astounded - doesn't comment it... |
Guess the next digits of this floating point number. Where does it came from?
> 4.9292683 |
What Is The Next Digit? |
## 6
It's $\pi e \gamma$
Thanks to the [Inverse Symbolic Calculator](http://isc.carma.newcastle.edu.au/standardCalc?input=4.9292683). |
The six-pack is a thing of the past. Beverages of the future will use the seven-pack format. But how will the mighty spacemen of the future manage to ship the Slurm seven-pack efficiently in rectangular space crates?
Below is a schematic of the seven-pack. How can a seven-pack of this shape completely fill a rectan... |
Miss Danner, a primary school teacher, is on her way to school - it's the first day of school this year.
In class, she sees two identically looking boys sitting in the first row.
>Aw, twins, so cute!
she exclaims.
>We aren't twins.
the boys respond unisono.
Miss Danner - astounded - doesn't comment it... |
The six-pack is a thing of the past. Beverages of the future will use the seven-pack format. But how will the mighty spacemen of the future manage to ship the Slurm seven-pack efficiently in rectangular space crates?
Below is a schematic of the seven-pack. How can you completely fill a rectangle using seven-packs o... |
The six-pack is a thing of the past. Beverages of the future will use the seven-pack format. But how will the mighty spacemen of the future manage to ship the Slurm seven-pack efficiently in rectangular space crates?
Below is a schematic of the seven-pack. How can you completely fill a rectangle using seven-packs o... |
The six-pack is a thing of the past. Beverages of the future will use the seven-pack format. But how will the mighty spacemen of the future manage to ship the Slurm seven-pack efficiently in rectangular space crates?
Below is a schematic of the seven-pack. How can you completely fill a rectangle using seven-packs o... |
The six-pack is a thing of the past. Beverages of the future will use the seven-pack format. But how will the mighty spacemen of the future manage to ship the Slurm seven-pack efficiently in rectangular space crates?
Below is a schematic of the seven-pack. How can you completely fill a rectangle using seven-packs o... |
The new land surveyor and his boss arrived at the work site, a huge and perfectly flat parking lot. His boss said, "Your first assignment is going to be a tough one. You see this parking lot? It has light posts every 50 feet east to west and north to south."
"A perfect Cartesian grid with a light post at each int... |
In a set of puzzles I found online recently, I acquired this unnamed puzzle:
![spherical puzzle][1]
I'm not sure what it is, or how to solve it. It definitely comes apart, as it is split into six pieces, but I see no way to begin disassembly or, for that matter, start assembling it again.
Pushing on pieces doe... |
How do I solve this put-together spherical puzzle? |
In a set of puzzles I found online recently, I acquired this unnamed puzzle:
![spherical puzzle][1] ![rotated spherical puzzle][2]
I'm not sure what it is, or how to solve it. It definitely comes apart, as it is split into six pieces, but I see no way to begin disassembly or, for that matter, start assembling it ... |
In a set of puzzles I found online recently, I acquired this unnamed puzzle:
![spherical puzzle][1] ![rotated spherical puzzle][2]
I'm not sure what it is, or how to solve it. It definitely comes apart, as it is split into six pieces, but I see no way to begin disassembly or, for that matter, start assembling it ... |
Well, funny story.
My friend grew irritated with the dern plastic thing, so he threw it at a wall. And guess what? It fell apart.
Inside, the disassembly instructions read:
> HOW TO DISASSEMBLE:
> To disassemble, throw the ball at the ground.
I'm not kidding.
----
The re-assembly is actually pretty... |
Well, funny story.
My friend grew irritated with the dern plastic thing, so he threw it at a wall. And guess what? It fell apart.
Inside, the disassembly instructions read:
> HOW TO DISASSEMBLE:
> To disassemble, throw the ball at the ground.
I'm not kidding.
![enter image description here][1]
Ther... |
Well, funny story.
My friend grew irritated with the dern plastic thing, so he threw it at a wall. And guess what? It fell apart.
Inside, the disassembly instructions read:
> HOW TO DISASSEMBLE:
> To disassemble, throw the ball at the ground.
I'm not kidding.
![enter image description here][1]
Ther... |
Inspired by this thread: [Largest possible tile in 2048][1], I've always wondered with such games to what extent you NEED luck to be able to get to a high score. For example, the maximum tile of 131072 requires the luck to spawn a '4' tile in the last free square on the board.
What often seems to screw you over, mi... |
Hint 1
>! The game _is_ possible. I have completed it.
>! As you have guessed, the aim of the game is to assemble each dot with the 2 matching rings.
Hint 2
>! One of the positive reviews on the Android store speaks about _lateral thinking_ and _think outside of the box_. Have you done that?
Hint 3
>! If, w... |
![Isaac Asimov's Science Fiction Magazine, spring 1977][cover]
I found the following puzzle by Martin Gardner in an archived copy of _[Isaac Asimov's Science Fiction Magazine][arch]_. I've heard it before, but in a more vulgar setting, involving condoms instead of gloves. I think mr. Gardner knew this version too, h... |
A guy lives in the 10nth floor of an apartment building.
On a normal day he goes to the 5th floor with the elevator and then climbs the remaining 5 floors.
On a rainy day he goes to the 10th floor directly.
Why ? |
Hint 1
>! The game _is_ possible. I have completed it.
>! As you have guessed, the aim of the game is to assemble each dot with the 2 matching rings.
Hint 2
>! One of the positive reviews on the Android store speaks about _lateral thinking_ and _think outside of the box_. Have you done that?
Hint 3
>! If, w... |
The game _is_ possible. I have completed it.
As you have guessed, the aim of the game is to assemble each dot with the 2 matching rings.
Hint 1
>! Sorry, I cannot explain you how the pieces moves. I haven't figures everything out. But some general patterns were enough to solve it. Don't loose your time over ... |
A young boy is taking a ride with his dad when a truck runs them off the road, killing the father and critically injuring the young boy. He's Medivac'd to the nearest hospital as the child is lying on the table ready for operation, the surgeon looks at the boy and says "I cannot operate on him, he's my son.
How is t... |
In 1980, Jack has an age of 20. In 1985 however, he is only 15 years old.
How did Jack age backwards? |
**M = 9,999,999,999,999**
Depending on how constrained you are I can see a solution where any number up to 9,999,999,999,999 or even larger.
Simply put the stones that must be thrown each turn are the delimiters for the numbers being sent. Each spy will wait a number of seconds, or minutes if seconds seems to... |
**M = 9,999,999,999,999**
Depending on how constrained you are I can see a solution where any number up to 9,999,999,999,999 or even larger.
Simply put the stones that must be thrown each turn are the delimiters for the numbers being sent. Each spy will wait a number of seconds, or minutes if seconds seems to... |
This was inspired by http://puzzling.stackexchange.com/questions/2432/a-curious-case-of-benjamin-button but has a different solution.
In 1980 AD (or 1980 CE, if you prefer), Jack has an age of 20. In 1985 however, he is only 6 years old.
How did Jack age backwards?
|
**M = 9,999,999,999,999**
Depending on how constrained you are I can see a solution where any number up to 9,999,999,999,999 or even larger.
Simply put the stones that must be thrown each turn are the delimiters for the numbers being sent. Each spy will wait a number of seconds, or minutes if seconds seems to... |
**M = 9,999,999,999,999**
Depending on how constrained you are I can see a solution where any number up to 9,999,999,999,999 or even larger.
Simply put the stones that must be thrown each turn are the delimiters for the numbers being sent. Each spy will wait a number of seconds, or minutes if seconds seems to... |
For people who don't like this answer i have a lower bound answer for **m = 4096**.
Simple use the dividers between the 13 stones from above as a binary word. This will allow numbers up to 2^12 to be represented. By considering the division of a group as a binary signal, and the lack of a divider as the off po... |
For people who don't like this answer i have a lower bound answer for **m = 81**.
Simple use the dividers between the 13 stones from above as a binary word. This will allow numbers up to 2^12 to be represented. By considering the division of a group as a binary signal, and the lack of a divider as the off positi... |
For people who don't like this answer i have a lower bound answer for **m = 81**.
Simple use the dividers between the 13 stones from above as a binary word. This will allow numbers up to 2^12 to be represented. By considering the division of a group as a binary signal, and the lack of a divider as the off positi... |
The king had a mutant rat problem in his kingdom, so he ordered 3 young men to go down under the depth of the ground to find the cause. The 3 young men jumped down the hole, and followed the tunnel. After hours of walking, they met an intersection. There were 4 paths at this intersection. The king had told them before ... |
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.
... |
Most of my awareness of puzzles and puzzle games has come from a decade of haphazardly stumbling around the internet. There's a flavor/genre that I particularly enjoy, but I haven't had much luck finding more of them - or even nailing down to correct terms to find them. Lo and behold, I finally stumbled across [this qu... |
How do I find more enigmatic, no-clues-given puzzles? |
For people who don't like my old answer i have a lower bound answer for **m = 81**.
Lets look at the restraint.
1) The number of stones is the only information that may be collected.
2) The two spies must take turns , they must therefore take the same number of turns
3) The number of stones is limited , 2... |
Most of my awareness of puzzles and puzzle games has come from a decade of haphazardly stumbling around the internet. There's a flavor/genre that I particularly enjoy, but I haven't had much luck finding more of them - or even nailing down to correct terms to find them. Lo and behold, I finally stumbled across [this qu... |
There are 53 lions in a cage and 1 goat. All the lions are very hungry and would want to eat the goat. But the problem here is that any lion who eats the goat can satisfy his hunger but he will himself become a goat and then other lions will eat him. All lions are intelligent and understand this fact, so obviously no o... |
Let's follow the usual approach for this.
Say there's just 1 lion and the goat. Would the lion eat the goat? Yes, it's not at risk.
So say there's 2 lions and a goat. Would a lion eat the goat? If so it would become the goat in the 1 lion and a goat situation, and so it would be eaten. So it would not eat the goa... |
I expect multiple answers to this, however only 1 of them is correct.
A bus was scheduled to stop 10 times today. Each time, 7 people got on, and 5 got off.
At the last stop, how many people were in the bus before the driver kicked them off? |
I expect multiple answers to this, however only 1 of them is correct.
A bus was scheduled to stop 10 times today. Each time, 7 people got on the bus, and 5 got off.
At the last stop, how many people were in the bus before the driver kicked them off? |
A top secret facility is guarded by 1 man, this man will kill anyone with the wrong, or without a, passcode.
There are 5 spies. They have determined the code is one of the following;
1. Orange
2. Apple
3. Red
4. 5
5. TV
6. Complicator
Each spy guessed in the order they tried.
The last spy g... |
Where to manufacture a 3D wood puzzle? |
You are given some matches, a rope, and a pair of scissors. The rope burns irregularly and takes 60 minutes to burn end to end; however, we know that the burn rate a distance `x` from the left end is the same as the burn rate a distance `x` from the right.
What is the minimum time interval you can measure? |
What is the shortest known rubik's cube algorithm? |
Here's a part of the sequence:
A
B
C
D
E
1113122113
311311222113
...
The letters are the missing members (there are 5 missing members) and **A** is the first member of the sequence. The last member presented is not the end of the sequence, it can go on forever.
The sequen... |
There are 3 talking hats on the table. Each can ask 2 questions, to either hat. 1 of them speaks only truth. 1 speaks only lies. 1 can speak only when spoken to, he will speak at random.
How can the 3 hats talk to each other in such a way as to distinguish who's the truth speaker, lie teller, and random chatter? |
There are 3 talking hats on the table. Each can ask 2 questions, to either hat. 1 of them speaks only truth. 1 speaks only lies. 1 can speak only when spoken to, he will speak at random.
YOU know who's who just fine. But you cannot tell the hats. You can only tell the "truth speaker" a question to ask one of the oth... |
There are 3 talking hats on the table. Each can ask 2 questions, to either hat. 1 of them speaks only truth. 1 speaks only lies. 1 can speak only when spoken to, he will speak at random.
YOU know who's who just fine. But you cannot tell the hats. You can only tell the "truth speaker" a question to ask one of the oth... |
Peter found an old piece of paper that an equation was written on it. Some of **digits** or **operations** are unreadable. Help Peter to complete the **balanced** equation.
![enter image description here][1]
The equation is: $87+?3?12-4?2=?36-15??1/?$
Source: My Brain
[1]: https://i.stack.imgur.com/zTn2... |
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