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There are four prisoners. All four prisoners will be freed if at least one of them guesses the color of the hat on his head. They can't speak, and they can't touch each other. Number 1 sees number 2 and 3's hats. Number 2 sees number 3's hat. Number 3 sees only the wall. Number 4 sees only the wall. T...
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...
My back yard forms a rectangular grid of squares except some of the squares are missing as they are covered by pipes or a small tree. The layout is as follows. A 'x' indicates a square that is free and '.' a covered square. . x x . . x x x . x x x x x x x x x x x x x x x x x x x ...
All numbers between 1 and 10<sup>10</sup> are written out and compiled into a dictionary (as the only entries). **What is the first uneven number?**
All numbers between 1 and 10<sup>10</sup> are written out and ordered alphabetically into a dictionary (as the only entries). Spaces and hyphens are removed. **What is the first odd number?**
All numbers between 1 and 10<sup>10</sup> are written out and ordered alphabetically into a dictionary (as the only entries). Spaces and hyphens are removed. 1024 would then be "onethousandfortytwo". **What are the first odd number and the first prime number?**
All numbers between 1 and 10<sup>10</sup> are written out and ordered alphabetically into a dictionary (as the only entries). Spaces and hyphens are removed. 1024 would then be "onethousandfortytwo". Also, "and" is not being used as a link (I think that's American English). **What the first odd number and wh...
All numbers between 1 and 10<sup>10</sup> are written out and ordered alphabetically into a dictionary (as the only entries). Spaces and hyphens are removed. 1024 would then be "onethousandfortytwo". Also, "and" is not being used as a link (I think that's American English). **What the first odd number?** <...
All numbers between 1 and 10<sup>10</sup> are written out and ordered alphabetically into a dictionary (as the only entries). Spaces and hyphens are removed. 1024 would then be "onethousandtwentyfour". Also, "and" is not being used as a link (I think that's American English). **What the first odd number?** ...
All numbers between 1 and 10<sup>10</sup> are written out and ordered alphabetically into a dictionary (as the only entries). Spaces and hyphens are removed. 1024 would then be "one<b>thousand</b>twentyfour". Also, "and" is not being used as a link (I think that's American English). **What is the first odd nu...
All numbers between 1 and 10<sup>10</sup> are written out and ordered alphabetically into a dictionary (as the only entries). Spaces and hyphens are removed. 1024 would then be "one<b>thousand</b>twentyfour". Also, "and" is not being used as a link (I think that's American English). Furthermore, the American ...
All numbers between 1 and 10<sup>10</sup> are written out and ordered alphabetically into a dictionary (as the only entries). Spaces and hyphens are removed. 1024 would then be "one<b>thousand</b>twentyfour". Also, "and" is not being used as a link (I think that's American English). Furthermore, the American ...
What is the appropriate answer to this question? > **What is the first natural number, which can not be defined with less than 15 words?** > Explanations: 1. Natural means integers greater than 0. 2. Word here is any group of letters separated by spaces or punctuation. "a", "of", for example, are words too....
This is not a very difficult problem, but it seems that it hasn't been asked here. It's one of my favorite, so here we go: > I am twice as old as you were when I was as old as you are.<br /> > The sum of our ages is 81.<br /> > How old are we?
This is not a very difficult problem, but it seems that it hasn't been asked here. It's one of my favorite, so here we go: > I am twice as old as you were when I was as old as you are.<br /> > When you will be as old as I am, the sum of our ages will be 81.<br /> > How old are we? --- Edit: I totally misrem...
Number words in the given range are assembled from the following components: * The set $A$ of single digits: `eight`, `five`, `four`, `nine`, `one`, `seven`, `six`, `three`, `two`. * The set $B$ of double-digit blocks: `eighteen`, `eleven`, `fifteen`, `fourteen`, `nineteen`, `seventeen`, `sixteen`, `thirteen`, `t...
All numbers between 1 and 10<sup>10</sup> are written out and ordered alphabetically into a dictionary (as the only entries). Spaces and hyphens are removed. 1024 would then be "one<b>thousand</b>twentyfour". Also, "and" is not being used as a link (I think that's American English). Furthermore, the American ...
Linguistic hardness ($LH$) of a natural number ($N>0$) is the ratio of the amount of letters in the writing of this number in English to the amount of its digits. For example, $LH(1234) = 7.75$: Number of letters (one thousand two hundred thirty four) / Number of digits $(1234) = 31/4 = 7.75$. What is the number ...
Linguistic hardness ($LH$) of a natural number ($N>0$) is the ratio of the amount of letters in the writing of this number in English to the amount of its digits. For example, $LH(1234) = 7.75$: Number of letters (one thousand two hundred thirty four) / Number of digits $(1234) = 31/4 = 7.75$. What is the $N<10^9...
Linguistic hardness ($LH$) of a natural number is the ratio of the amount of letters in the writing of this number in English to the amount of its digits. For example, $LH(1234) = 7.75$: Number of letters (one thousand two hundred thirty four) / Number of digits $(1234) = 31/4 = 7.75$. What is $N: 0<N<10^9$ with ...
The Tale of Genji is a classic japanese novel, probably written more than a thousand years ago. The 19th century artist Toyohara Kunichika painted a picture for every of the [54 chapters](http://www.man-pai.com/Genji/genji.htm). Every [picture](http://www.man-pai.com/Grandes_series/Kunichika_54sentimentos/kunichika_...
The Tale of Genji is a classic japanese novel, probably written more than a thousand years ago. The 19th century artist Toyohara Kunichika painted a picture for every of the [54 chapters](http://www.man-pai.com/Genji/genji.htm). Every [picture](http://www.man-pai.com/Grandes_series/Kunichika_54sentimentos/kunichika_...
The Tale of Genji is a classic japanese novel, probably written more than a thousand years ago. The 19th century artist Toyohara Kunichika painted a picture for every of the [54 chapters](http://www.man-pai.com/Genji/genji.htm). Every [picture](http://www.man-pai.com/Grandes_series/Kunichika_54sentimentos/kunichika_...
The Tale of Genji is a classic japanese novel, probably written more than a thousand years ago. The 19th century artist Toyohara Kunichika painted a picture for every of the [54 chapters](http://www.man-pai.com/Genji/genji.htm). Every [picture](http://www.man-pai.com/Grandes_series/Kunichika_54sentimentos/kunichika_...
The Tale of Genji is a classic japanese novel, probably written more than a thousand years ago. The 19th century artist Toyohara Kunichika painted a picture for every of the [54 chapters](http://www.man-pai.com/Genji/genji.htm). Every [picture](http://www.man-pai.com/Grandes_series/Kunichika_54sentimentos/kunichika_...
The Tale of Genji is a classic japanese novel, probably written more than a thousand years ago. The 19th century artist Toyohara Kunichika painted a picture for every of the [54 chapters](http://www.man-pai.com/Genji/genji.htm). Every [picture](http://www.man-pai.com/Grandes_series/Kunichika_54sentimentos/kunichika_...
The Tale of Genji is a classic japanese novel, probably written more than a thousand years ago. The 19th century artist Toyohara Kunichika painted a picture for every of the [54 chapters](http://www.man-pai.com/Genji/genji.htm). Every [picture](http://www.man-pai.com/Grandes_series/Kunichika_54sentimentos/kunichika_...
The Tale of Genji is a classic japanese novel, probably written more than a thousand years ago. The 19th century artist Toyohara Kunichika painted a picture for every of the [54 chapters](http://www.man-pai.com/Genji/genji.htm). Every [picture](http://www.man-pai.com/Grandes_series/Kunichika_54sentimentos/kunichika_...
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...
##The Magic Hexagon Problem## ![Magic Hexagon][1] > A magic hexagon of order $n$ is an arrangement of close-packed hexagons containing the numbers $1, 2, ..., H_{n-1}$, where $H_n$ is the $n^{th}$ hex number such that the numbers along each straight line add up to the same sum. (Here, the hex numbers are i.e., $1...
This question appeared in an old math contest, and I seem to remember that the answer I had back when I first saw it was unsatisfactory. > You have a deck of cards numbered from $1$ to $60$. First, you shuffle them, and deal them out into six rows of ten cards each. Then, you do the following two things: > 1. You...
The Tale of Genji is a classic japanese novel, probably written more than a thousand years ago. The 19th century artist Toyohara Kunichika painted a picture for every of the [54 chapters](http://www.man-pai.com/Genji/genji.htm). Every [picture](http://www.man-pai.com/Grandes_series/Kunichika_54sentimentos/kunichika_...
What do the glyphs in the Tale of Genji (genjimon) mean?
he linguistic hardness ($LH$) of a natural number is the ratio of the amount of letters in the writing of this number in English to the amount of its digits. For example, $LH(1234) = 7.75$, as: $$\frac{\mbox{Number of letters}}{\mbox{Number of digits}} = \frac{\mbox{(one thousand two hundred thirty four)}}{1234...
What is the number with the largest linguistic hardness less than $10^9$?
What do the Glyphs from the Tale of Genji represent?
Ok - you want your Algorithm to create more challenging mazes? Change it to a BFS - You start with your normal algorithm, but you always pick random where you continue and not just after you have reached the goal... 1. Initialize path-list with one active square at the starting location. 2. Pick a random ac...
The following is a paraphrasing of a problem from Martin Gardner called "Tricky Track." Three schools $-$ $A,B,C$ $-$ participated in a track meet with several events. Each school was awarded some amount of points for each event (a positive integer). Each event was scored in the same way, and of course the first pla...
The Tale of Genji is a classic japanese novel, probably written more than a thousand years ago. The 19th century artist Toyohara Kunichika painted a picture for every of the [54 chapters](http://www.man-pai.com/Genji/genji.htm). Every [picture](http://www.man-pai.com/Grandes_series/Kunichika_54sentimentos/kunichika_...
Which of these intervals can you not measure given two sand timers (which change from question to question)? There are no minute marks, halfway points, etc. A. 7 minutes with a 4- and 5-minute timer B. 15 minutes with a 7- and 11-minute timer C. 14 minutes with a 5- and 8-minute timer Hint: There may be mo...
You've probably heard about challenges with water jugs, so why not try a few? 1. Use 3- and 5- liter jugs to get 4 liters. <br/> 2. Use 5- and 7- liter jugs to get 4 liters. <br/> 3. This one's different. How many different exact measurements can you get using only 8- and 11- liter jugs (not including 0 liters...
What is the "linguistically hardest" number less than $10^9$?
![enter image description here][1] You are given two of each from the array of 8 vegetables numbered 1 to 8 as shown above. So in total you have 16 veggies(8 pairs). Your task is to make the longest kebab (sequence of vegetables arranged linearly) such that the number of vegetable between any pair of vegetables sho...
A piece of fabric shaped like a regular hexagon with unit-length sides is given, with vertices A...F and center O. Let a *fold* correspond to folding some fabric along a straight line, without stretching. For example, bringing A to E and B to D by folding along line FC is a fold. Let a *uniform folding* be a series ...
A piece of fabric shaped like a regular hexagon with unit-length sides is given, with vertices A...F and center O. Let a *fold* correspond to folding some fabric along a straight line, without stretching. For example, bringing A to E and B to D by folding along line FC is a fold. Let a *uniform folding* be a series ...
Given L units of wash water, we want to wash out a vessel (eg, a milk bottle, honey jar, chemistry flask...) using a series of rinses that minimize the amount of Stuff other than water remaining in the jar. Suppose R units of liquid remain in the vessel each time we pour out the rinse; and suppose the original conce...
Given L units of wash water, we want to wash out a vessel (eg, a milk bottle, honey jar, chemistry flask...) using a series of rinses that minimize the amount of Stuff other than water remaining in the jar. Suppose R units of liquid remain in the vessel each time we pour out the rinse; and suppose the original conce...
Given $L$ units of wash water, we want to wash out a vessel (eg, a milk bottle, honey jar, chemistry flask...) using a series of rinses that minimize the amount of Stuff other than water remaining in the jar. Suppose $R$ units of liquid remain in the vessel each time we pour out the rinse; and suppose the original c...
Given $L$ units of wash water, we want to wash out a vessel (eg, a milk bottle, honey jar, chemistry flask...) using a series of rinses that minimize the amount of Stuff other than water remaining in the jar. Suppose $R$ units of liquid remain in the vessel each time we pour out the rinse; and suppose the original c...
to my knowledge this puzzle is not previously published (except by me on google+ recently), would be interested to hear of any info otherwise. this following graph was generated using a simple ruby program and gnuplot. it graphs a "basic/ fundamental" number theoretic property of the natural numbers. can you figure ...
obviously I understand the definition part "One who will succeed". But can someone tell me how the word play part works in this clue? "with melody, we hear"
An $S$-*tileset* is a collection of $n$ oriented tiles, where no two tiles have the same size, each tile is one unit thick, and its non-zero-integer length and width add up to $n+1$. (So, an $S$-tileset has $n$ tiles, of sizes $1\times n, 2\times{n-1}, ... n\times1$.) You can make a tower of tiles by stacking up lay...
How high a tower of tiles can be made?
An $S$-*tileset* is a collection of $n$ oriented tiles, where no two tiles have the same size, each tile is one unit thick, and its non-zero-integer length and width add up to $n+1$. (So, an $S$-tileset has $n$ tiles, of sizes $1\times n, 2\times{n-1}, ... n\times1$.) You can make a tower of tiles by stacking up lay...
An $S$-*tileset* is a collection of $n$ oriented tiles, where no two tiles have the same size, each tile is one unit thick, and its non-zero-integer length and width add up to $n+1$. (So, an $S$-tileset has $n$ tiles, of sizes $1\times n, 2\times{n-1}, ... n\times1$.) You can make a tower of tiles by stacking up lay...
If you multiply $2178$ by $4$ you will get the same digits, but written in the back order, like if you look in a mirror: $2178 \cdot 4 = 8712$. **How to find all possible natural numbers, that are mirrored when multiplied by 4?** **What other factors $F \neq 4$ have mirrored numbers?** I see that $F = 1$ has a...
The image shows numbers on ring-dials on a curiously-geared combination lock, where the current setting is (3,3,3,3) and ring sizes are (5,7,8,11), inner to outer. The setting (0,0,0,0) opens the lock. When you rotate any ring, rings outside it move twice as fast in the same direction, while rings inside it move tw...
First, what do we know about this puzzle? - There are 5*7*8*11 = 3080 possible positions. - Moves do not affect each other, so if you have a good set of moves, you can do them in any order. Given this, it is a relatively simple algorithm to find the shortest sequence of moves. What I did was to start with a...
First, what do we know about this puzzle? - There are 5*7*8*11 = 3080 possible positions. - Moves do not affect each other, so if you have a good set of moves, you can do them in any order. - There must be at least one move of the 8 ring, but not necessarily any of the others. Given this, it is a relatively ...
i made a program for it, and it's algorithm is to get the number from user, reverse it and do the multiplication, if the reverse and multiplication is equall then print it for you. here is a C# code: Console.WriteLine("number from"); int a = Convert.ToInt32(Console.ReadLine()); Console.WriteLine(...
there is a running match, but there isn't anyone to judge, and we have only information that the audience gave us and we know there info is true.we have color, name their rank and T-shirt number. here it is: 1.**Mahsa** won and she had worn red T-Shirt. 2.the girl who worn T-Shirt number 1 became 3rd in match. ...
Who? What Color? Rank? Number?
You say there were 4 runners and that Mahsa, who was wearing a red shirt, came first, right? Then how come hint no. 3 mentions contradictory info? As stated by you, "Mahnaz who defeat a girl with red T-Shirt didn't wear number 2.", the girl wearing a red shirt gets defeated by Mahnaz. Plus you've also mentioned 4 colo...
there is a running match, but there isn't anyone to judge, and we have only information that the audience gave us and we know there info is true.we have color, name their rank and T-shirt number. here it is: 1.**Mahsa** won and she had worn red T-Shirt. 2.the girl who worn T-Shirt number 1 became 3rd in match. ...
If you multiply $2178$ by $4$ you will get the same digits, but written in the back order, like if you look in a mirror: $2178 \cdot 4 = 8712$. How to find all possible natural numbers, that are mirrored when multiplied by 4? **And prove that these are all numbers.** **What other factors $F \neq 4$ have mirrored ...
in the picture below can you draw 6 straight lines that passes all the circles? as soon as you start drawing lines you can't take your pen up until you draw all six lines. ![enter image description here][1] [1]: https://i.stack.imgur.com/eFRcz.jpg
in the picture below can you draw 6 straight lines that passes all the circles? as soon as you start drawing lines you can't take your pen up until you draw all six lines. hint: you don't have to keep the polyline inside the square ![enter image description here][1] [1]: https://i.stack.imgur.com/eFRc...
> #Names in Boxes > - The names of 100 prisoners are placed in 100 wooden boxes, one name to a box, and the boxes are lined up on a table in a room. > - One by one, the prisoners are led into the room; each may look in at most 50 boxes, but must leave the room exactly as he found it > and is permitted...
Why not this? This one also does what he wants. ![][1] [1]: https://i.stack.imgur.com/qZltr.jpg
How many squares can you find in the pattern?
10 squares that are $1$x$1$ (trivial) 4 squares that are $\sqrt{2}$x$\sqrt{2}$ (Diamonds centered at the 4 central circles) 2 squares that are $\sqrt{5}$x$\sqrt{5}$ (Each starts at a yellow circle. Move like a knight: example 2 right 1 up, 2 up 1 left, 2 left 1 down, 2 down 1 right) 2 squares that are $\sq...
9 squares that are $1$x$1$ (trivial) 4 squares that are $\sqrt{2}$x$\sqrt{2}$ (Diamonds centered at the 4 central circles) 2 squares that are $\sqrt{5}$x$\sqrt{5}$ (Each starts at a yellow circle. Move like a knight: example 2 right 1 up, 2 up 1 left, 2 left 1 down, 2 down 1 right) 2 squares that are $\sqr...
First, what do we know about this puzzle? - There are 5*7*8*11 = 3080 possible positions. - Moves do not affect each other, so if you have a good set of moves, you can do them in any order. - There must be at least one move of the 8 ring, but not necessarily any of the others. Given this, it is a relatively ...
There is a running match, but there isn't anyone to judge; we have only information that the audience gave us (but we know their info is true). We the have name, rank, T-shirt color, and T-shirt number of each runner, as follows: 1. **Mahsa** won and she wore a red T-Shirt. 2. The girl who wore T-Shirt number 1 f...
>You have three cakes of diameter 20cm, 16cm and 12cm respectively as shown in the figure. ![enter image description here][1] They all have the same height. Now your task is to divide these 3 cakes into 4 equal parts and you are only allowed to cut one cake at a time. >**What is the minimum number of cuts ...
Divide 3 cakes into 4 equal parts?
>You have three cakes of diameter 20cm, 16cm and 12cm respectively as shown in the figure. ![enter image description here][1] They all have the same height. Now your task is to divide these 3 cakes into 4 equal parts and you are only allowed to cut one cake at a time. >**What is the minimum number of cuts re...
>You have three cakes of diameter 20cm, 16cm and 12cm respectively as shown in the figure. ![enter image description here][1] They all have the same height. Now your task is to divide these 3 cakes into 4 equal parts and you are only allowed to cut one cake at a time. >**What is the minimum number of cuts re...
How many sqares can you draw in the pattern, when each corner of a sqare has to lie in the exact center of one of the 20 colored circles? ![enter image description here][1] [1]: https://i.stack.imgur.com/ZxzBH.jpg
How many squares can you draw in the pattern?
![enter image description here][1] [1]: https://i.stack.imgur.com/8hBJR.jpg How about put the 12cm cake on top of the 16cm cake and make a cut like this?
Consider a line segment of length _L_. This segment is cut in three segments at arbitrary points. What is the probability that these three segments could be rearranged as sides of a triangle?![Example][1] [1]: https://i.stack.imgur.com/9Sm1x.png
If I have a table of binary values, and tell you the column and row counts for "on" or "1" values, is it possible to solve, with certainty, any grid of size n*m? Take the following puzzle for example: | 4 | 5 | 3 | 2 | 1 ---|---|---|---|---|--- 3 | ? | ? | ? | ? | ? 2 | ? | ? | ? | ? | ? ...
It was late night when Markus was sitting at his desk and suddenly a fairy appeared out of nowhere. She told him that he had been granted a wish. Markus wished for her to tell him next week's lottery draw and handed her pen and paper. But the fairy told him that these were 6 wishes and that thus it was not possible for...
I found a puzzle on a programming site where it was given password hints and one has to think what is the correct password. One hint was "Was wir wissen, ist ein Ozean; was wir nicht wissen, ist ein Tropfen." How can I solve it?
I found a puzzle on a programming site where it was given password hints and one has to think what is the correct password. One hint was >Was wir wissen, ist ein Ozean; >was wir nicht wissen, ist ein Tropfen. How can I solve it?
It was late night when Markus was sitting at his desk and suddenly a fairy appeared out of nowhere. She told him that he had been granted a wish. Markus wished for her to tell him next week's lottery draw and handed her pen and paper. But the fairy told him that these were 6 wishes and that thus it was not possible for...
I couldn't find a trick to solve this because I don't know a formula for "possibilities of summands." So I wrote a program and tried to brute force a solution. There turn out to be many or I am mistaken... Let's go step by step. Suppose the sum is 21 there is only one possible drawing: 1,2,3,4,5,6. The order of the ...
It was late night when Markus was sitting at his desk and suddenly a fairy appeared out of nowhere. She told him that he had been granted a wish. Markus wished for her to tell him next week's lottery draw and handed her pen and paper. But the fairy told him that these were 6 wishes and that thus it was not possible for...
It was late night when Markus was sitting at his desk and suddenly a fairy appeared out of nowhere. She told him that he had been granted a wish. Markus wished for her to tell him next week's lottery draw and handed her pen and paper. But the fairy told him that these were 6 wishes and that thus it was not possible for...
It was late night when Markus was sitting at his desk and suddenly a fairy appeared out of nowhere. She told him that he had been granted a wish. Markus wished for her to tell him next week's lottery draw and handed her pen and paper. But the fairy told him that these were 6 wishes and that thus it was not possible for...
It was late night when Markus was sitting at his desk and suddenly a fairy appeared out of nowhere. She told him that he had been granted a wish. Markus wished for her to tell him next week's lottery draw and handed her pen and paper. But the fairy told him that these were 6 wishes and that thus it was not possible for...
It was late night when Markus was sitting at his desk and suddenly a fairy appeared out of nowhere. She told him that he had been granted a wish. Markus wished for her to tell him next week's lottery draw and handed her pen and paper. But the fairy told him that these were 6 wishes and that thus it was not possible for...
I found a puzzle on a programming site where it was given password hints and one has to think what is the correct password. One hint was >Was wir wissen, ist ein Ozean; >was wir nicht wissen, ist ein Tropfen. How can I solve it? EDIT: Here is the source of the site: <!DOCTYPE html> <head> ...
## The riddle ## Randall Munroe (of [xkcd][xkcd] fame) has, a bit hidden on his site, [a logic puzzle] [xkcd_q]: > A group of people with assorted eye colors live on an island. They are > all perfect logicians -- if a conclusion can be logically deduced, > they will do it instantly. No one knows the color of th...
A dwarf-killing giant lines up 10 dwarfs from shortest to tallest. Each dwarf can see all the shortest dwarfs in front of him, but cannot see the dwarfs behind himself. The giant randomly puts a white or black hat on each dwarf. No dwarf can see their own hat. The giant tells all the dwarfs that he will ask each dwar...
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 need help understanding the solution to the following puzzle: **Puzzle:** There is a "triangular" duel between the three shooters. Everyone shoots one by one, can shoot once and any person he wants. Smith always hits the target (100%) and shoots last. Brown hits the target 80% of the time and shoots second. Jones ...
I would like to ask if anyone has seen elsewhere this variation on the standard truth tellers/liars kind of puzzle. In the usual repertoire it is assumed that every person questioned knows the answer to every question asked. We now assume that this need not be the case; and that if a truth-teller is asked a questio...