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> What is the solution for this puzzle from IQ [test][1]?
>![enter image description here][2]
[1]: http://iqtest.dk/main.swf
[2]: https://www.braingames.ru/forum/uploads/post-13114-1262532170.jpg |
What is the solution for this puzzle from this [IQ test][1]?
>![enter image description here][2]
[1]: http://iqtest.dk/main.swf
[2]: https://www.braingames.ru/forum/uploads/post-13114-1262532170.jpg |
I was doing a Sudoku puzzle (in my morning newspaper on the train to work) and got stuck at this point:
_ _ _ _ 4 _ 7 2 1
4 _ 2 6 _ 7 _ 8 9
7 _ _ 8 _ 2 _ _ _
2 9 5 4 6 8 _ _ 7
3 4 6 5 7 1 8 9 2
8 _ _ _ _ 9 6 4 5
_ 2 _ 7 _ 4 _ _ 3
5 _ _ ... |
How can I spot an X-Wing? |
There is a puzzle which I remember from many years ago which can be summarised as
> It is easy to arrange 20 items in five rows of four items, but how could you arrange just 10 items in five rows of four items?
The answer is this (spoiler-protected for those of you who want to try to solve it first):
>! 
The gist of it is, every time you enter a room, you have to leave it... |
This "puzzle" can be described as an _Euler Trail_, and was discussed in a video by James Grime in which he proves why the puzzle is impossible:
* [YouTube: A Maths Puzzle: Euler Trail and Solution ](https://www.youtube.com/watch?v=CQNH2ifOAQE)
The gist of it is, every time you enter a room, you have to leave it... |
As far as I can tell there are no doors in this image, therefore any line will cross every doors and no line will cross a door twice: just draw a line anywhere. Actually you might have already draw some lines of length 0.
EDIT: some people seem to think this is a troll, maybe they simply don't know what [universal](... |
I have written a Delphi application to brute force a solution. Unfortunately I see no way of solving the problem: what expression(s) results in number N? That is I see no solution other than generating all expressions and then seeing what natural numbers they result in.
So I can't really help with Bobson's crowd-sou... |
I have written a Delphi application to brute force a solution. Unfortunately I see no way of solving the problem: what expression(s) results in number N? That is I see no solution other than generating all expressions and then seeing what natural numbers they result in.
So I can't really help with Bobson's crowd-sou... |
I have written a Delphi application to brute force a solution. Unfortunately I see no way of solving the problem: what expression(s) results in number N? That is I see no solution other than generating all expressions and then seeing what natural numbers they result in.
So I can't really help with Bobson's crowd-sou... |
Going to throw this out there. I like the "APE" explanation much better, but maybe someone can do something with this.
"Trap" can be used as a synonym for equipment (though not a common one). If "Circus" is the general clue, leading to "Trapeze", then the rest of it might be "Equipment" = trap and "has chimpanzee, s... |
I have written a Delphi application to brute force a solution. Unfortunately I see no way of solving the problem: what expression(s) results in number N? That is I see no solution other than generating all expressions and then seeing what natural numbers they result in.
So I can't really help with Bobson's crowd-sou... |
What would be a chess position, where a player (white or black) has a maximum possible number of different moves to make?
There are two options:
1. The position must be possible to obtain in a chess game.
2. Any position, involving any number of chess pieced are allowed. (Most probably it is optimal to fill ... |
I've highlighted the X-Wing and the 9's involved in this X-Wing:
![enter image description here][1]
[1]: https://i.stack.imgur.com/rQqKf.png
See how's there's two 9's in row 3 and also two 9's in row 8? (highlighted in blue)
Since every row must contain exactly one 9, either A and D must both be 9 OR B ... |
I've highlighted the X-Wing and the 9's involved in this X-Wing:
![enter image description here][1]
[1]: https://i.stack.imgur.com/rQqKf.png
See how's there's two 9's in row 3 and also two 9's in row 8? (highlighted in blue)
Since every row must contain exactly one 9, either A and D must both be 9 OR B ... |
I've highlighted the X-Wing and the 9's involved in this X-Wing:
![enter image description here][1]
[1]: https://i.stack.imgur.com/rQqKf.png
See how's there's two 9's in row 3 and also two 9's in row 8? (highlighted in blue)
Since every row must contain exactly one 9, either A and D must both be 9 OR B ... |
I have written a Delphi application to brute force a solution. Unfortunately I see no way of solving the problem: what expression(s) results in number N? That is I see no solution other than generating all expressions and then seeing what natural numbers they result in.
So I can't really help with Bobson's crowd-sou... |
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 = ... |
This is from the current weekly math challenge from the newspaper *Le Monde*.
> Alice and Bob play the following game, in turn:
> a number between $1$ and $10$ is written on a blackboard.
> At each of their turn, they can either
> * multiply the current number by $3$
> * multiply the current number by $... |
This is from the current weekly math challenge from the newspaper *Le Monde*.
> Alice and Bob play the following game, in turn:
> a number between $1$ and $10$ is written on a blackboard.
> At each of their turn, they choose **one** of these actions:
> * multiply the current number by $3$
> * multiply t... |
This is from the current weekly math challenge from the newspaper *Le Monde*.
> Alice and Bob play the following game, in turn:
> a number between $1$ and $10$ is written on a blackboard.
> At each of their turn, they choose **one** of these actions:
> * multiply the current number by $3$
> * multiply t... |
I have written a Delphi application to brute force a solution. Unfortunately I see no way of solving the problem: what expression(s) results in number N? That is I see no solution other than generating all expressions and then seeing what natural numbers they result in.
So I can't really help with Bobson's crowd-sou... |
Slightly tongue-in-cheek, but a variation on the "maybe" option provided the other player interprets it literally enough.
Keep evaluating powers of your number until you reach one that exceeds 6. Is it an odd power? Answer yes = 2, no = 3, infinitely long pause = 1 ... |
The following problem is found in the first Norwegian arithmetic, published in 1645 by Tyge Hansøn:
Three hundred oxen large and small,
A cattle owner wanted to buy:
3 for 63 daler he got.
Again, he let them sell,
3 for 63 daler they fetched,
both slim and fat.
787$1\over 2$ daler was his profit. ... |
The following problem is found in the first Norwegian arithmetic, published in 1645 by Tyge Hansøn:
> Three hundred oxen large and small,
> A cattle owner wanted to buy:
> 3 for 63 daler he got.
> Again, he let them sell,
> 3 for 63 daler they fetched,
> both slim and fat.
> 787$1\over 2$ daler was... |
`This statement contains 3 0's, 1 1, 4 2's, 1 3, 5 4's 92 5's, 6 6's, 53 7's, 58 8's, and 9 9's.`
Clearly that statement is incorrect. It only has 1 occurrence of the character "0", not 3; and there are definitely not 92 instances of "5".
Can you rewrite it to make it true? You still must list all 10 digits.
... |
`This statement contains 3 0's, 1 1, 4 2's, 1 3, 5 4's 92 5's, 6 6's, 53 7's, 58 8's, and 9 9's.`
Clearly that statement is incorrect. It only has 1 occurrence of the character "0", not 3; and there are definitely not 92 instances of "5".
Can you rewrite it to make it true? You still must follow the same format,... |
`This statement contains 3 0's, 1 1, 4 2's, 1 3, 5 4's 92 5's, 6 6's, 53 7's, 58 8's, and 9 9's.`
Clearly that statement is incorrect. It only has 1 occurrence of the character "0", not 3; and there are definitely not 92 instances of "5".
Can you rewrite it to make it true? You still must follow the same format,... |
Following this question: http://puzzling.stackexchange.com/q/1901/28 I wonder what if we allow to change number of digits and folmulate task like this:
> Write statement like "This statement contains $M_0$ 0's, $M_1$ 1, ..., $M_N$ N's", which is true.
**What is the smallest $N$ possible here?**
___________
Sim... |
What is smallest N to complite the task "Write a true self-reflective statement about the digits from 0 to N"? |
Following this question: http://puzzling.stackexchange.com/q/1901/28 I wonder what if we allow to change number of digits and folmulate task like this:
> Write statement like "This statement contains $M_0$ 0's, $M_1$ 1, ..., $M_N$ N's", which is true. You must write about all digits, which statement includes: that a... |
This is probably my favorite puzzle. It uses logic, but it's not one of those "logic table" puzzles which i dislike immensely. What is this type of puzzle called and are there more like it that are not just variants?
Three children are playing on the beach and all three have mud on their foreheads. An old man walks ... |
Who has mud on their forehead? |
This is probably my favorite puzzle. It uses logic, but it's not one of those "logic table" puzzles which i dislike immensely. What is this type of puzzle called and are there more like it that are not just variants?
> Three children are playing on the beach and all three have mud on their foreheads. An old man walk... |
There is no special name for such type of puzzles as far as i know.
But usually they are formulated in terms of hats worn by logicians.
If you google you can find a lot of puzzles of this type, for example, [this][1]:
> The Logical Hats Puzzle. Logicians A, B and C each wear a hat with a positive integer on i... |
Remove first or last letter - What is the name of this word puzzle/type of word? |
In general, these puzzles are called "Deletion Puzzles" but the usually do not include the restriction to the beginning or end letters. The most famous example is "startling" as it is the longest. It is also sometimes called "Elision". Please not that these terms also do not require it to be iterative.
"Terminal D... |
1. Two workers A and B manufactured a batch of identical parts. A worked
for 2 hours and B worked for 5 hours and they did half the job. Then they
worked together for another 3 hours and they had to do (1/20)th of the
job. How much time does B take to complete the job, if he worked alone?
A) 24 hours
B) 12 hours
... |
Can anyone explain me how to solve this problem? |
> There is 100 white and 101 black balls. Balls of the same colour looks the same. White balls are numbered from lighter to heavier (from 1 to 100). The same is true for black balls (they are numbered from 1 to 101).
> **What is minimal number of weightings to find the ball with the middle weight?** (That is the bal... |
It was traditional during the times of the Oregon Trail that men founding new towns were allowed to stake their claim on land upon arriving to the west coast during the gold rush.
Suppose a man is given $n$ minutes to stake his claim on an area of land defined by the [convex hull][1] of those stakes placed into th... |
It was traditional during the times of the Oregon Trail that men founding new towns were allowed to stake their claim on land upon arriving to the west coast during the gold rush.
Suppose a man is given $n$ minutes to stake his claim on an area of land defined by the [convex hull][1] of those stakes placed into th... |
It was traditional during the times of the Oregon Trail and the gold rush that men founding new towns were allowed to stake their claim on land upon arriving to the west coast.
Suppose a man is given $n$ minutes to stake his claim on an area of land defined by the [convex hull][1] of those stakes placed into the g... |
It was traditional during the times of the Oregon Trail and the gold rush that men founding new towns were allowed to stake their claim on land upon arriving to the west coast.
Suppose a man is given $n$ minutes to stake his claim on an area of land defined by the [convex hull][1] of those stakes placed into the g... |
> There is 100 white and 101 black balls. Balls of the same colour looks the same. White balls are numbered from lighter to heavier (from 1 to 100). The same is true for black balls (they are numbered from 1 to 101).
> **What is minimal number of weightings on balance scale to find the ball with the middle weight?**... |
It was traditional during the times of the Oregon Trail and the gold rush that men founding new towns were allowed to stake their claim on land upon arriving to the west coast.
Suppose a man is given $n$ minutes to stake his claim on an area of land defined by the [convex hull][1] of those stakes placed into the g... |
It was traditional during the times of the Oregon Trail and the gold rush that men founding new towns were allowed to stake their claim on land upon arriving to the west coast.
Suppose a man is given $n$ minutes to stake his claim on an area of land defined by the [convex hull][1] of those stakes placed into the g... |
It is clear that the area must be a polygon with stakes at corners.
I do not have prove, but **most probably**:
1. The fastest way to put stake it each corner is to follow perimeter of the polygon. Then the figure with maximum aria and fixed perimeter is circle. The aria would be $S = \pi(\frac{n}{2\pi})^2 = \fra... |
It was traditional during the times of the Oregon Trail and the gold rush that men founding new towns were allowed to stake their claim on land upon arriving to the west coast.
Suppose a man is given $n$ minutes to stake his claim on an area of land defined by the [convex hull][1] of those stakes placed into the g... |
**Currently this answer is given in assumption that you must go from last stake to the first. This is not exactly what is asked and I will need to rework it later.**
It is clear that the area must be a polygon with stakes at corners.
I do not have prove, but **most probably**:
1. The fastest way to put stake ... |
**Currently this answer is given in assumption that you must go from last stake to the first. This is not exactly what is asked and I will need to rework it later.**
It is clear that the area must be a polygon with stakes at corners.
I do not have prove, but **most probably**:
1. The fastest way to put stake ... |
> There is 100 white and 101 black balls. All balls have different weight. Balls of the same colour looks the same. White balls are numbered from lighter to heavier (from 1 to 100). The same is true for black balls (they are numbered from 1 to 101).
> **What is minimal number of weightings on balance scale to find t... |
Two workers A and B manufactured a batch of identical parts. A worked
for 2 hours and B worked for 5 hours and they did half the job. Then they
worked together for another 3 hours and they had to do (1/20)th of the
job. How much time does B take to complete the job, if he worked alone?
- A) 24 hours
- B) 12 hour... |
It is clear that the area must be a polygon with stakes at corners.
I do not have prove, but **most probably**:
1. The fastest way to put stake it each corner is to follow perimeter of the polygon. So we must optimise an area between the path and a line (which goes through first and last stake). The maximum are... |
It is clear that the area must be a polygon with stakes at corners.
I do not have prove, but **most probably**:
1. The fastest way to put stake it each corner is to follow perimeter of the polygon. So we must optimise an area between the path and a line (which goes through first and last stake). The maximum are... |
There is a problem from M.Gardner book *("Wheels, Life, and other Mathematical Amusements", p. 201)*:
> One needs to put some number (finite, bigger than 1) of points on a plane with the following constrain: When one takes any 2 points, then build segment on them, then build perpendicular bisector line, there is exa... |
Is there a second solution to points and perpendicular bisectors problem? |
> There are 100 white and 101 black balls. All the balls have different weights. Balls of the same colour look the same. White balls are numbered from lighter to heavier (from 1 to 100). The same is true for black balls (they are numbered from 1 to 101).
> **What is the minimal number of weightings on a balance scal... |
There is a problem from M.Gardner book *("Wheels, Life, and other Mathematical Amusements", p. 201)*:
> One needs to put some number (finite, bigger than 1) of points on a plane with the following constrain: When one takes any 2 points, then build segment on them, then build perpendicular bisector line, there is exa... |
How many subset intersections do you require? |
There is a problem from M.Gardner book *("Wheels, Life, and other Mathematical Amusements", p. 201)*:
> One needs to put some number (finite, bigger than 1) of points on a plane with the following constrain: When one takes any 2 points, then build segment on them, then build perpendicular bisector line, there is exa... |
I wanted a solution that avoids uncertainty. So here's a good logical contradiction:
> Is exactly one of these statements true?
> (a) Your number is not 2.
> (b) Your number is 3 and your answer to this question is Yes.
**Analysis**
If the number is 1, then (a) is true and (b) is false, so the answer is ... |
As you can see in this topic, there are a lot of possible solutions of course.
But there is **general solution**, which includes all of them. It is:
> Are you thinking of 1 OR you are thinking of 2 AND [statement with unknown result]?
The interpretation of the answer is clear:
1 -> yes
2 -> I do n... |
There is a problem from M.Gardner book *("Wheels, Life, and other Mathematical Amusements", p. 201)*:
> [Hallard T. Croft] asked if there existed a finite set of points on the plane such that the perpendicular bisector of the line segment joining any two points would always pass through at least two other points of ... |
There is no special name for such type of puzzles as far as i know.
But usually they are formulated in terms of hats worn by logicians.
If you google you can find a lot of puzzles of this type, for example, [this][1]:
> The Logical Hats Puzzle. Logicians A, B and C each wear a hat with a positive integer on i... |
There are many **Brainfuck** variations used in puzzles in geocaching, for example **Ook!** They are usually not so hard to decode because they are 'standards' - therefore the substitution is googlable, there are often online converter.
But what is general strategy to dealing with such puzzles, if the only thing I k... |
Is there a general strategy for decoding Braifuck mutations? |
There are many **Brainfuck** variations used in puzzles in geocaching, for example **Ook!** They are usually not so hard to decode because they are 'standards' - therefore the substitution is googlable, there are often online converter.
But what is general strategy to dealing with such puzzles, if the only thing I k... |
Whats the solution to these puzzles?
You are supposed to draw in the dented boxes what the missing figure is for each of the five puzzles, the small symbols in top left are just the numbering of the test.
Warning: These are extremely hard until you see the solution
![enter image description here][1]
[... |
Is there a general strategy for decoding Brainfuck mutations? |
[Countdown](http://en.wikipedia.org/wiki/Countdown_%28game_show%29) is a British game show in which people try and make words out of nine given letters or reach a target number using six given numbers and basic arithmetic within 30 seconds.
In the numbers round, the players choose numbers from groups of "large" and ... |
What's the largest number that can be obtained in the process of solving a numbers game on Countdown? |
[Countdown](http://en.wikipedia.org/wiki/Countdown_%28game_show%29) is a British game show in which people try and make words out of nine given letters or reach a target number using six given numbers and basic arithmetic within 30 seconds.
In the numbers round, the players choose numbers from groups of "large" and ... |
Concerning the question "is there a set of given numbers and a target number that requires even larger numbers as part of the solution?"
I can not guarantee that there is not other possible way to achieve the target, but, here we get $62500 $ as an intermediate result:
$834 = \frac{25\cdot 5\cdot 5\cdot 100+50}{7... |
Concerning the question "is there a set of given numbers and a target number that requires even larger numbers as part of the solution?"
Yes, there is. Here we get $62550$ as an intermediate result:
$834 = \frac{25\cdot 5\cdot 5\cdot 100+50}{75} = \frac{62550}{75}$
According to *Lopsy* there is no other possib... |
[Countdown](http://en.wikipedia.org/wiki/Countdown_%28game_show%29) is a British game show in which people try and make words out of nine given letters or reach a target number using six given numbers and basic arithmetic within 30 seconds.
In the numbers round, the players choose numbers from groups of "large" and ... |
One summer day John was jogging in the countryside wearing only his normal running clothes (shorts, vest, sports shoes and socks). After running for some time he saw that the lace of one of sports shoes was untied. While he was bending down to tie it up, a psychopath who was hidden nearby, approached him from behind ... |
The following puzzles were [created][1] by Robert Lato to measure IQ in range between 160 and 190.
Whats the solution to them?
> You are supposed to draw in the dented boxes what the missing figure is for each of the five puzzles, the small symbols in top left are just the numbering of the test.
>![enter ima... |
The following puzzles were [created][1] by Robert Lato to measure IQ in range between 160 and 190.
Whats the solution to them?
**These have tormented me for a long time, I will gladly pay 10$ per solution.**
> You are supposed to draw in the dented boxes what the missing figure is for each of the five puzzl... |
As with klm123, I don't know of a specific name for this type of problem (oracle riddle?). However, I've usually seen this question in the context of [an island with people of two eye colors and an oracle](https://xkcd.com/blue_eyes.html).
In this case, the old man is the oracle, whether or not the children have mu... |
The following puzzles were [created][1] by Robert Lato to measure IQ in range between 160 and 190.
Whats the solution to them?
> You are supposed to draw in the dented boxes what the missing figure is for each of the five puzzles, the small symbols in top left are just the numbering of the test.
>![enter ima... |
Since we don't have any visual cues to measure the end orientation, John needs some way to judge how much he rotated. That'd require very good timekeeping and some way to measure the angular acceleration. We'll assume that John has perfect mental and physical skills and can track time, angular displacement, etc exactly... |
Picture this.
You are in a hallway of a very large office building.
Near you are 50 light switches of which 3 are unlabled. These lightswitches are connected to 3 lights in 3 separate rooms. The rooms are not directly in your line of sight as there are 47 other rooms too.
This makes it that walking up and dow... |
I've seen this puzzle with men and coloured hats. The way it was framed was in stages, which led the reader (by the nose) to the solution of the most complex case.
The puzzle was simple - there are three men, all wearing hats, and a diabolical king. The hats are either white or black. The men can see each other's... |
It depends on what you mean by the wording of the sentences: Does "There is 1 wrong sentence on this sheet" mean "There is exactly 1 wrong sentence on this sheet," or does it mean "There exists 1 wrong sentence on this sheet (but there may be more)"?
If it is the first case, the answer is **99**, because there are 1... |
Epimenides (a Cretan) once wrote a poem, in which he stated that all Cretans are liars.
Since he is a Cretan, and therefore a liar, Cretans are veracious.
But then again he wouldn't be a liar!
This paradox can be solved, i.e. it can be shown that it's not an actual paradox. How?
|
Epimenides (a Cretan) once wrote a poem, in which he stated that all Cretans are liars.
Since he is a Cretan, and therefore a liar, Cretans are veracious.
But then again he wouldn't be a liar!
This paradox can be solved, i.e. it can be shown that it's not an actual paradox. How?
Edit: In this puzzle's "univ... |
Epimenides (a Cretan) once wrote a poem, in which he stated that all Cretans are liars.
Since he is a Cretan, and therefore a liar, Cretans are veracious.
But then again he wouldn't be a liar!
This paradox can be solved, i.e. it can be shown that it's not an actual paradox. How?
Edit: In this puzzle's "univ... |
Epimenides (a Cretan) once wrote a poem, in which he stated that all Cretans are liars.
Since he is a Cretan, and therefore a liar, Cretans are veracious.
But then again he wouldn't be a liar!
This paradox can be solved, i.e. it can be shown that it's not an actual paradox. How?
Edit: In this puzzle's "univ... |
I am sorry for I do not exactly know the name of this puzzle.
My question is:
In a 3x3 grid, I'd have to put numbers from 1 to 9 in a manner so that respective row,column and diagonal add up to 15.
I have only been able to come up with one solution:
6 1 8
7 5 3
2 9 4
Through some calculations and tr... |
You are kidnapped and your offender plays a game with you. In front of you are 2 boxes, one with 50 white balls, and another with 50 black balls. The kidnapper will pull out a ball from one of the two boxes, at random. If the ball is white you survive, if not, you are shot.
#Rules:
- Every ball must be in one of... |
It is impossible.
Quite the same problem is "[Seven Bridges of Königsberg][1]", it was solved (proven) by Euler.
1. Suppose you have drawn such a line and follow it from one room to another. Since you must use each door you must have a look at each room out of 5. What are these rooms?
2. There will be 3 (at ... |
You are given ten stacks of golden coins, each stack consisting of ten coins and a digital scale with arbitrary precision. You know that all stacks of coins are made from gold, weighing 10 grams per coin except one stack, which is made from silver but is pained golden. A silver coin weighs 1 gram less than a golden one... |
In a 3x3 grid, I'd have to put numbers from 1 to 9 in a manner so that respective row, column and diagonal add up to 15.
I have only been able to come up with one solution:
6 1 8
7 5 3
2 9 4
Through some calculations and trial and error method.
Is there any strategy or way of approach to thi... |
I insist on using all the digits!
>! (1 + 1^1234567890 + 1)! = 6
>!
>! (2 + (2^1234567890 % 2)!)! = 6
>!
>! (3 + 3^1234567890 % 3)! = 6
>!
>! (4 - (4^1234567890 % 4)!)! = 6
>!
>! 5 + (5^1234567890 % 5)! = 6
>!
>! 6 + 6^1234567890 % 6 = 6
>!
>! 7 - (7^1234567890 % 7)! = 6
... |
There is a type of puzzle which can be modelled as finding a [Hamiltonian path][1] through a graph. One example is the [Icosian game][2]. What factors affect the difficulty of such puzzles, to be solved by humans? Let's assume the solver is unfamiliar with graph theory and Hamiltonian paths in particular, but can see t... |
What factors affect the difficulty of Hamiltonian puzzles? |
The critical factor is the connectivity of the graph. The Hamiltonian path problem is known to be NP-complete. Years ago I saw charts from a talk called "Where are all the hard problems?" (seems no longer available) The point was that although Hamiltonian path is NP-complete, specific instances are easy. Either (fo... |
There are four prisoners.
All four prisoners will be free if at least one of them will guess the color of the hat on his head.
They can't speak (only for say hats color), they can't touch.
Number 1 sees number 2 and 3 hats.
Number 2 sees number 3 hat.
Number 3 sees only the wall.
Number 4 sees only... |
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