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How do you create a general locked-box problem? |
You could decide to partition the corners and use one for each level, writing even smaller numbers. Or tilting the numbers at different angles. But that sounds boring, why not use Arabic, Roman and Persian/Farsi (oops, there is some digit overlap) numerals at each level?
I consider sudoku puzzles that legitimately r... |
Oh my. For large N ( > 400) this gets an exponential structure of strings of carnage that can be stopped at certain points: a simple strategy exists for each pirate of fierceness 400+100*2^n (negative n allowed until we start getting fractional pirates). No optimal strategy exists for the remaining leaders; they die.
... |
You could decide to partition the corners and use one for each level, writing even smaller numbers. Or tilting the numbers at different angles. But that sounds boring, why not use Arabic, Roman and Persian/Farsi (oops, there is some digit overlap) numerals at each level?
I consider sudoku puzzles that legitimately r... |
I have already figured out how to generate sudoku grids, like this one:
5 6 7 2 3 8 1 4 9
4 8 9 7 6 1 3 5 2
2 3 1 9 5 4 6 8 7
1 7 5 6 8 9 2 3 4
8 4 3 1 2 5 9 7 6
9 2 6 3 4 7 5 1 8
3 9 4 8 1 6 7 2 5
7 1 8 5 9 2 4 6 3
6 5 2 4 7 3 8 9 1
Now, I need to make it an a... |
What is a simple and efficient way of removing numbers from a full sudoku puzzle to create one with a single unique solution? |
How, as a writer of riddles, can I rate their difficulty?
I guess, for me alone, knowing the answer even before the riddle existed, it's pretty much impossible, and I should need some external help. Are there some riddling communities or something like that, who could help rate the difficulty? How would I approach t... |
How to rate difficulty of a classic riddle? |
Leonhard Euler proved that it is impossible to solve this puzzle:
The challenge is to take a walk around the area depicted, and cross each bridge (yellow) *exactly* once. Using topology, Euler proved that ... |
Are there any topology puzzled similar to The Seven Bridges of Königsberg? |
> Nearly all the Times crossword grids have rotational symmetry: they
> can be rotated 180 degrees and remain identical. Rarely, puzzles with
> only vertical or horizontal symmetry can be found; yet rarer are
> asymmetrical puzzles, usually when an unusual theme requires breaking
> the symmetry rule. **This rule ha... |
N logicians are wearing hats which can be of N different colors (each hat has one color; there can be multiple hats with the same color). Each logician can see the colors of all hats except his own. The logicians must simultaneously call out a color; they win if at least one logician calls the color of his own hat. The... |
Quality crossword puzzles have had a [rotational symmetry requirement][1] for a very long time. It was determined early on in the development of the puzzle that the symmetry rule (along with the fully checked and all-over interlock rules) made the puzzles more interesting. (IMHO, that is because it puts interesting con... |
How to solve 5-10 letter anagrams (without a computer or electronic)? |
Say there are
5 logicians `1, 2, 3, 4, 5`
& 5 colors `A, B, C, D, E`
One of the logician, say A, is chosen the leader. Everyone will call out the leader's hat color. The leader will call out the color that is missing from the remaining N-1 hat colors he can see. Two cases are possible:
If there is no repeat... |
In [this question](http://puzzling.stackexchange.com/questions/112/the-puzzle-of-the-locked-box), I presented a puzzle involving seven locks, with a Grand Vizier and four slaves.
But I would like to use this style of puzzle in some of my own secret-unlocking riddles, in order to require that a person solve a specifi... |
Here's another oldie from a book, slightly paraphrased to make it more quantitative.
> You're in a room with a ceiling exactly 100 feet high. Two thin but sturdy ropes are hanging from hooks at the ceiling and just touch the ground. You can climb these ropes, but there is nothing else to climb on. Equipped with only... |
Here's another oldie from a book, slightly paraphrased to make it more quantitative.
> You're in a room with a ceiling exactly 100 feet high. Two thin but sturdy ropes are hanging from hooks at the ceiling and just touch the ground. You can climb these ropes, but there is nothing else to climb on. Equipped with only... |
[It is known](http://puzzling.stackexchange.com/questions/100/minimum-number-of-squares-for-a-sudoku-puzzle) that the minimum number of clues a sudoku must have to have a unique solution is 17. But on every website I've seen for them, I haven't found any that are rotationally symmetrical (of order 2).
I once saw a p... |
What is the fewest number of clues on a rotationally symmetrical sudoku grid with a unique solution? |
Here's another oldie from a book, slightly paraphrased to make it more quantitative.
> You're in a room with a ceiling exactly 100 feet high. Two thin but sturdy ropes are hanging from fixed hooks at the ceiling and just touch the ground, close enough that you can grab both of them at the same time comfortably. You ... |
[It is known](http://puzzling.stackexchange.com/questions/100/minimum-number-of-squares-for-a-sudoku-puzzle) that the minimum number of clues a sudoku must have to have a unique solution is 17. But on every website I've seen for them, I haven't found any that are rotationally symmetrical.
I once saw a puzzle in a bo... |
In a sudoku puzzle, what is the absolute minimum number of clues that must be given to specify a layout with a unique solution? Is one in each row, column, and box (9 total) necessary or sufficient?
|
It is known that 17 clues are necessary to uniquely specify a sudoku puzzle. For how many puzzles is 17 sufficient? From the history of the minimal proof, I gather that there are multiple puzzles for which it is enough. Is 17 enough to specify *any* unique-solution sudoku? Just a class or a few classes of puzzles? |
How many minimal-clue sudoku puzzles are there? |
[This book](http://books.google.ca/books?id=U6RpAgAAQBAJ&pg=PA111) appears to have a puzzle with only 18 clues that is rotationally symmetrical.
7 2 . . . . . . .
. 5 . . . 9 . . .
. . . . 3 8 . . .
. . . 4 . . 5 . .
. . 3 . . . 9 . .
. . 1 . . 3 . . .
. . . 2 5 . . . .
. . . 6... |
In order to construct the solution to this problem in the general space, it's helpful to ignore the Grand Vizier. The Grand Vizier can hold all the keys except one, which all the slaves hold, and that answers that component minimally.
I have discovered a generic method for generating solutions to these puzzles given... |
If you use the Beginners' Method to solve the Rubik's cube, and solve the equator layer (the layer between the U-layer and D-layer), it can happen that one of the edges is flipped, like this:
![Flipped edge in Equator layer][1]
<sup>Screenshot generated using Cube Explorer</sup>
A way to solve this is to repla... |
It is known that 17 clues are necessary to uniquely specify a sudoku puzzle. For how many puzzles is 17 sufficient? From the history of the minimal proof, I gather that there are multiple puzzles for which it is enough. Is 17 enough to uniquely specify *every* sudoku? Just a class or a few classes of puzzles? |
It is known that there are a minimum of 17 clues needed to create a [proper sudoku puzzle](http://en.wikipedia.org/wiki/Mathematics_of_Sudoku#Minimum_number_of_givens). For how many puzzles is 17 sufficient? From the history of the minimal proof, I gather that there are multiple puzzles for which it is enough. Is 17 en... |
It is known that there are a minimum of 17 clues (filled squares) needed to create a [proper sudoku puzzle](http://en.wikipedia.org/wiki/Mathematics_of_Sudoku#Minimum_number_of_givens) ( (One that has a unique solution).
For how many puzzles is 17 sufficient? From the history of the minimal proof, I gather that ther... |
It is known that there are a minimum of 17 clues needed to create a [proper sudoku puzzle](http://en.wikipedia.org/wiki/Mathematics_of_Sudoku#Minimum_number_of_givens).
For how many puzzles is 17 sufficient? From the history of the minimal proof, I gather that there are multiple puzzles for which 17 clues are enough... |
<sup>**Note**: This is a follow-up question to [Burning ropes as timers](http://puzzling.stackexchange.com/questions/166/burning-ropes-as-timers). The following question and its answers may contain spoilers.</sup>
To sum up the puzzle, these are the rules (slightly modified):
- You have some number *N* of ropes, ... |
Burning ropes as timers - How many time intervals can be measured? |
Suppose you have a chessboard with two opposite corner squares removed, like this:
![mutilated chessboard][1]
Can you move a pawn on the board only horizontally and vertically, one square at a time, and have it touch every square exactly once?
[1]: https://i.stack.imgur.com/AEqI3.gif |
You are given twelve identical-looking balls and a two-sided scale. One of the balls is of a different weight, although you don't know whether it's lighter or heavier. How can you use just three weighings of the scale to determine not only what the different ball is, but also whether it's lighter or heavier? |
In order to construct the solution to this problem in the general space, it's helpful to ignore the Grand Vizier. The Grand Vizier can hold all the keys except one, which all the slaves hold, and that answers that component minimally.
I have discovered a generic method for generating solutions to these puzzles given... |
Suppose you want to create a set of weights so that any object with an integer weight from 1 to 40 pounds can be balanced on a two-sided scale by placing a certain combination of these weights onto that scale.
What is the fewest number of weights you need, and what are their weights? |
What's the fewest weights you need to balance any weight from 1 to 40 pounds? |
I've tried to begin solving a cryptogram by making educated guesses from the context: position of punctuation, the presence of single-letter words, or assumptions about the frequency of the letter E, for a few examples. I often find 2-letter and 3-letter words in the puzzle and am looking for a more logical approach to... |
How do I choose between letter possibilities for 2- and 3-letter words in a cryptogram? |
The magic square is a well-known grid of the numbers from 1 to 9 in which every row, column, and diagonal adds up to 15:
4 9 2
3 5 7
8 1 6
But it is also possible to create magic squares using other numbers:
24 87 45
73 52 31
59 17 80
It's also known that given just a few filled-... |
What is the fewest number of filled-in squares required to uniquely define a magic square? |
It's called [Bridg-It][1], or [Game of Gale][2] (as it was invented by David Gale). It is the rectangular grid equivalent of the [Shannon switching game][3], which is a generalized version of [Hex][4].
[1]: http://en.wikipedia.org/wiki/Bridg-It#Gale
[2]: http://www.papg.com/show?1TPI
[3]: http://en.wikiped... |
How can I solve 5-10 letter anagrams without a computer or electronics?
I was paying the Word Scramble category in the game _Quiz Up_ and found it complicated, only in some parts. At home, I used an anagram solver, but elsewhere my friends have aced me in this section.
I searched on the internet and found [this... |
How to solve 5-10 letter anagrams (without a computer or electronics)? |
I, being a fan of 2048, was wondering if anyone has any proven strategies for playing [2048](http://gabrielecirulli.github.io/2048)?
Please only write 1 tip or strategy per answer, so they can be isolated as good or bad.
|
I know the puzzles and riddles were as popular if not more in the ancient times. (let us put a hard limit on 'ancient times' as predating the end of fall of the Roman Empire, around A.D. 470). Many of them survived to this day, e.g. the Sphinx Riddle ("What animal walks on four legs in the morning, two at noon, and thr... |
Are there any puzzles/riddles left from ancient times, to which no answer is known nowadays? |
Is there an official name for visual puzzles based on observation skill? |
#Red or Black
There are 3 children sitting on three chairs. The children can only look forward and all were one hat. The hats are either black or red. They are a total of 5 hats, 3 are coloured red and 2 are coloured black. The child on chair A says: "I don't know what colour of the hat I have." Then the child on chai... |
#Red or Black
There are 3 children sitting on three chairs. The children can only look forward and all wear one hat. The hats are either black or red. They are a total of 5 hats, 3 are coloured red and 2 are coloured black. The child on chair A says: "I don't know what colour of the hat I have." Then the child on chai... |
A farmer is looking to hire some hired hands. His usual three hires are named Barry, Harry, and Larry.
He knows from hiring them before that:
- Working together, Barry and Harry can plow an acre in two hours.
- Working together, Barry and Larry can plow an acre in three hours.
- Working together, Harry and L... |
Are there any topology puzzles similar to The Seven Bridges of Königsberg? |
My friend once told me a logic puzzle along the lines of:
> A student asks a teacher what the ages of the teacher's three kids are. The teacher said, "the product of their ages is 72, and the sum of their ages is your [the student's] house number." The student thought about this for a while, then came back to the te... |
How do I tell the children's ages? |
**If the end of the world was supposed to come on 1st January 2100, what would be the chances that it would happen on a Sunday?**
>!I personally feel that if the world's going to end, it must be on a Monday morning. |
End of the world - on a Sunday? |
**If the end of the world was supposed to come on the first day of a new century, what would be the chances that it would happen on a Sunday?**
>!I personally feel that if the world's going to end, it must be on a Monday morning. |
The answer is slightly trickier than you might think at first - it has to do with a quirk in the calendar we currently use, the [Gregorian Calendar](https://en.wikipedia.org/wiki/Gregorian_calendar#Adoption).
The Gregorian Calendar was instated by Pope Gregory (hence the name) in 1582 to account for a slight dispari... |
If the end of the world was supposed to come on the first day of a new century, what would be the chances that it would happen on a Sunday? |
The [Four color theorem](https://en.wikipedia.org/wiki/Four_color_theorem) says that no more than four colors are required for any map. Can it be proven or disproved that 3 colors can be used for United States map? |
Is there a proof that a map of the United States requires 4 colors? |
Oskar van Deventer's Gear Shift is a somewhat difficult puzzle to figure out how to solve. The puzzle looks like this:
![enter image description here][1]
You can see a [video of it here](https://www.youtube.com/watch?v=yO6YCBKvhzI).
What is a simple, intuitive method for solving this puzzle? I'm sure the opti... |
How do I solve Oskar van Deventer's Gear Shift puzzle? |
There is another way to do this problem, that doesn't involve any sort of conditional branching at all. It is in fact possible to set a fixed weighing schedule beforehand and still determine which ball is lighter or heavier in just 3 weighings. I'll explain how below.
-----
The gist of problems like these is, how... |
The answer is slightly trickier than you might think at first - it has to do with a quirk in the calendar we currently use, the [Gregorian Calendar](https://en.wikipedia.org/wiki/Gregorian_calendar#Adoption).
The Gregorian Calendar was instated by Pope Gregory (hence the name) in 1582 to account for a slight dispari... |
See Daniel [10](http://mechon-mamre.org/p/pt/pt3410.htm):4 – [12](http://mechon-mamre.org/p/pt/pt3412.htm):9:
> **10** …
> <sup>14</sup> Now I am come to make thee understand what shall befall thy people in the end of days…
> **12** …
> <sup>8</sup> And I heard, but I understood not... |
I wonder how accurately I will have to work if I make a wooden burr puzzle out of square sticks as for example described in http://en.wikipedia.org/wiki/Burr_puzzle. Should the notches be exactly the width of the square sticks so that everything fits tight together or should I sand down the sticks a little or widen the... |
How exact must the pieces of a wooden burr puzzle be? |
I know there are several different standard methods to solve a Rubik's cube, some easier, some more straightforward. It is known that the minimum number of moves to guarantee a solution is 20. Which method comes closest to the theoretical minimum in fewest average moves from a randomized cube to a solution? What about... |
What is the most efficient method to solve a Rubik's cube? |
A somewhat well-known puzzle is described as such:
> You have a pile of 3,000 bananas. You wish to transport them to a place 1,000 miles away on the back of a camel; however, the camel can only carry a maximum of 1,000 bananas, and will eat one banana every mile it travels (and will not go anywhere if it does not ha... |
A somewhat well-known puzzle is described as such:
> You have a pile of 3,000 bananas. You wish to transport them to a place 1,000 miles away on the back of a camel; however, the camel can only carry a maximum of 1,000 bananas, and will eat one banana every mile it travels (and will not go anywhere if it does not ha... |
Of the following 5 strategies for getting started assembling a jigsaw puzzle:
- Assembling the border and connecting other pieces to it
- Working your way out from one corner
- Trying to assemble faces or other recognizable parts of the picture
- Picking a random piece and working your way out from it
-... |
Of these five aproaches to starting a jigsaw puzzle, which one is fastest? |
This is a problem I once found in a math textbook a tutor used with me.
> A group of explorers is trying to get from their base camp to another camp which is eight days' walk through the desert.
> However, each explorer can only carry five days' worth of supplies. How many explorers need to venture out to make su... |
Here is the puzzle:
> 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 their eyes. Every
> night at midnight, a ferry stops at the island. Any islanders who have
> fig... |
In the 100 blue eyes problem - why is the green eyed oracle necessary? |
[Here is the puzzle][xkcd]:
> 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 their eyes. Every
> night at midnight, a ferry stops at the island. Any islanders who hav... |
Quick summary of the Prisoner's Dilemma: Two criminals are charged with a crime. Each is given an opportunity by the police to confess.
- If they **both stay silent**, they don't have enough evidence to convict for much, and they both get **1 year** in prison
- If they **both confess**, they have a lot more evide... |
Two perfect logicians, Summer and Proctor, are told that integers `x` and `y` have been chosen such that `1 < x < y` and `x+y < 100`. Summer is given the value `x+y` and Proctor is given the value `x*y`. They then have the following conversation.
- Proctor: I cannot determine the two numbers.
- Summer: I knew... |
Suppose you have a chessboard with two opposite corner squares removed, like this:
![Mutilated chessboard][1]
Is it possible to place 31 dominoes of size 2x1 so as to cover all of these squares?
[1]: https://i.stack.imgur.com/Ln6nc.gif |
Two perfect logicians, Summer and Proctor, are told that integers `x` and `y` have been chosen such that `1 < x < y` and `x+y < 100`. Summer is given the value `x+y` and Proctor is given the value `x*y`. They then have the following conversation.
- Proctor: I cannot determine the two numbers.
- Summer: I knew... |
I was just thinking about this.
Let's say that we have a card deck with 54 cards and the nth card is flipped. We repeat a short process of cutting the deck directly in the middle, and putting them back by alternating cards. Like:
1 5 5
2 6 1
// // 6
///// 2
You repeat... |
The [first time](http://blog.codinghorror.com/the-problem-of-the-unfinished-game/) I encountered the [Boy or Girl paradox](http://en.wikipedia.org/wiki/Boy_or_Girl_paradox) I was struck by how ambigious all of the formulations in English are. As Wikipedia notes:
> Gardner argued that a "failure to specify the rando... |
How can the "Boy or Girl" paradox be worded unambiguously? |
A **lateral thinking puzzle** is a puzzle that involves thinking in ways outside of a challenger's preconception – that is, "thinking outside the box".
For example, take the following riddle:
> A boy and his father are driving on a road when suddenly their car crashes. They are both severely injured and tak... |
A calculation puzzle is one that involves numerical calculation of some sort. For example:
> A farmer raises cows and chickens. He has 48 animals with a total of 126 legs. How many of each animal does he have?
The answer is that he has 33 chickens and 15 cows, which requires algebra and calculation to derive. |
Many people are familiar with the story of [Archimedes submerging a crown in water](https://en.wikipedia.org/wiki/Archimedes#Discoveries_and_inventions) to identify if the volume of the crown was consistent with the volume of the same amount of gold. The test was to see if a lighter cheaper metal (like silver) was... |
Could a gold/{second metal} crown the be created that would pass the Archimedes test cost effectively? |
Of the following 5 strategies for getting started assembling a jigsaw puzzle:
- Assembling the border and connecting other pieces to it
- Working your way out from one corner
- Trying to assemble faces or other recognizable parts of the picture
- Picking a random piece and working your way out from it
-... |
Or phrased differently, are non-symmetrical Sudoku puzzles considered legal Sudoku? |
Is a 'legit' Sudoku puzzle supposed to be symmetrical? |
I was just thinking about this.
Let's say that we have a card deck with 54 cards and the nth card is flipped. We repeat a short process of cutting the deck directly in the middle, and putting them back by alternating cards. Like:
1 5 5
2 6 1
// // 6
// ... |
> Mr. Smith has two children. **Mr. Smith only tells you that** at least one of them is a boy. What is the probability that both children are boys?
I have added the part in bold, and this rids the problem of ambiguity. Mr. Smith has told you that, for his family, at least one of the two children is male.
This g... |
The classical boy/girl question is asked like this:
> I have two kids, and one of them is a boy. What is the probability that I have two boys?
The problem, as you said, is that the statement itself is intolerably ambiguous. The interpretation that most people think of (and correctly too, I'd say, taking linguisti... |
The classical boy/girl question is asked like this:
> I have two kids, and one of them is a boy. What is the probability that I have two boys?
The problem, as you said, is that the statement itself is incredibly ambiguous. The interpretation that most people think of (and correctly too, I'd say, taking linguistic... |
I was just thinking about this.
Let's say that we have a card deck with 54 cards and the nth card is flipped. We repeat a short process of cutting the deck directly in the middle, and putting them back by alternating cards. Like:
1 5 5
2 6 1
6
... |
Of these five approaches to starting a jigsaw puzzle, which one is fastest? |
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