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In this figure with two **non-congruent** equilateral triangles and three-fold rotational symmetry the distance between any two of the 6 edges is an integer. Can you give a solution? I know only one solution. If the two triangles are congruent the problem is much easier and there are many solutions. ![enter ima...
In this figure with two **non-congruent** equilateral triangles and three-fold rotational symmetry the distance between any two of the 6 edges is an integer. Can you give a solution? I know only one essential solution (the GCD of the distances should be 1). If the two triangles are congruent the problem is much ea...
In this figure with two **non-congruent** equilateral triangles and three-fold rotational symmetry the distance between any two of the 6 vertices is an integer. Can you give a solution? I know only one essential solution (the GCD of the distances should be 1). If the two triangles are congruent the problem is much...
Quite simply, may White castle in the below position? There is much more than what meets the eye! For the record, White pawns move up and Black pawns move down. **Nikita M. Plaksin & Michel Caillaud, Feenschach 05/1982, 3. Prize** [![enter image description here][1]][1] [1]: https://i.stack.imgur.com/Aq...
I think I can do it in >! **50 moves**, which can be shown to be optimal. How to achieve it: >!<p>First, try the following 32 positions. If one of them has a treasure, the other part can be found in three more moves in the worst case (by trying the four neighbors sequentially; you know it is in the fourth if i...
There are 6 missing black pieces, and since the black pawns haven't moved, the bishop at c8 must have been captured by white knight. That gives 5 pawn captures, and so by counting, the third white knight must have promoted at g7. That means the white knight at h8 must have been there before black pawn got into g6. ...
There are 6 missing black pieces, and since the black pawns haven't moved, the bishop at c8 must have been captured by white knight. That gives 5 pawn captures, and so by counting, the third white knight must have promoted at g7. That means the white knight at h8 must have been there before black pawn got into g6. ...
There are 6 missing black pieces, and since the black pawns haven't moved, the bishop at c8 must have been captured by white knight. That gives 5 pawn captures, and so by counting, the third white knight must have promoted at g7. That means the white knight at h8 must have been there before black pawn got into g6. ...
There are 6 missing black pieces, and since the black pawns haven't moved, the bishop at c8 must have been captured by white knight. That gives 5 pawn captures, and so by counting, the third white knight must have promoted at g7. That means the white knight at h8 must have been there before black pawn got into g6. ...
There are 6 missing black pieces, and since the black pawns haven't moved, the bishop at c8 must have been captured by white knight. That gives 5 pawn captures, and so by counting, the third white knight must have promoted at g7. That means the white knight at h8 must have been there before black pawn got into g6. ...
There are 6 missing black pieces, and since the black pawns haven't moved, the bishop at c8 must have been captured by white knight. That gives 5 pawn captures, and so by counting, the third white knight must have promoted at g7. That means the white knight at h8 must have been there before black pawn got into g6. ...
Can you place 3 queens and 2 rooks on a 8x8 chess board, such that every empty cell is under attack? Good luck!
Can you place 21 knights on a 11x11 chess board, such that every empty cell is under attack? Good luck! Here is a similar question for 10x10: https://puzzling.stackexchange.com/questions/90169/knights-covering-a-10x10-chess-board
Answers to the questions: >! ... >! 31. As a result of its shape, which variety of pasta is named after the Italian word for ‘butterfly’? **FARFALLE** >! 32. Which animal cell organelles break down macromolecules, repair cell membranes, and destroy invading viruses and bacteria? **LYSOSOME** >! 33. Which ...
There's a restaurant that's heard that Vowelburger™ riddles don't satiate like they used to, so it's decided to start selling more sophisticated burgers. The menu says they sell a ***False*** Vowelburger™, a ***Real*** Vowelburger™, and a ***Lookalike*** Vowelburger™. You know that each burger comes with three buns ...
I once got a letter from my younger sister. It reads :- > Hello brother, > > How are you? I am fine. I have seen you have given me a lot of gifts, thank you for that. Here's a present from my side. Since I like puzzles, I am giving you 3 notes with the letter as well. Do check it if you want. Happy Puzzling, hope ...
Answers to the questions: >! ... >! 31. As a result of its shape, which variety of pasta is named after the Italian word for ‘butterfly’? **FARFALLE** >! 32. Which animal cell organelles break down macromolecules, repair cell membranes, and destroy invading viruses and bacteria? **LYSOSOME** >! 33. Which ...
I have been unable to find a solution for this F2L case. It takes about 3 seconds to do, and I do it really slowly. Basically, the F2L case is solved, but the edge is inverted. [![picture][1]][1] The way I do it right now is that I take it out, split it up, and insert it in again. How can I complete this in t...
Answers to the questions: >! ... >! 31. As a result of its shape, which variety of pasta is named after the Italian word for ‘butterfly’? **FARFALLE** >! 32. Which animal cell organelles break down macromolecules, repair cell membranes, and destroy invading viruses and bacteria? **LYSOSOME** >! 33. Which ...
The sergeant was told >!**DONT RETURN HOME**! --- Answers to the questions: >! ... >! 31. As a result of its shape, which variety of pasta is named after the Italian word for ‘butterfly’? **FARFALLE** >! 32. Which animal cell organelles break down macromolecules, repair cell membranes, and destroy in...
The sergeant was told >!**DONT RETURN HOME**! --- Answers to the questions: >! ... >! 31. As a result of its shape, which variety of pasta is named after the Italian word for ‘butterfly’? **FARFALLE** >! 32. Which animal cell organelles break down macromolecules, repair cell membranes, and destroy in...
The sergeant was told >!**DONT RETURN HOME**! --- Answers to the questions: >! ... >! 31. As a result of its shape, which variety of pasta is named after the Italian word for ‘butterfly’? **FARFALLE** >! 32. Which animal cell organelles break down macromolecules, repair cell membranes, and destroy in...
The sergeant was told >!**DONT GO HOME**! --- Answers to the questions: >! ... >! 31. As a result of its shape, which variety of pasta is named after the Italian word for ‘butterfly’? **FARFALLE** >! 32. Which animal cell organelles break down macromolecules, repair cell membranes, and destroy invadi...
The sergeant was told >!**DONT GO HOME**! --- Answers to the questions: >! ... >! 31. As a result of its shape, which variety of pasta is named after the Italian word for ‘butterfly’? **FARFALLE** >! 32. Which animal cell organelles break down macromolecules, repair cell membranes, and destroy invadi...
<sub>This is in the spirit of the [What is a Word™/Phrase™][1] series started by [JLee][2] with a special brand of [Phrase™][3] and [Word™][4] puzzles.</sub> ----------- If a word conforms to a special rule, I call it a Nowerk Word™. Use the examples below to find the rule. | Nowerk Words™ | Not...
Three queens and two rooks can be placed on a chess board so that all empty squares are under attack, as has been shown here: https://puzzling.stackexchange.com/questions/107214/3-queens-and-2-rooks-covering-a-8x8-chess-board. What if we require that all squares are under attack, even those occupied by any of the fi...
Three queens and two rooks can be placed on a chess board so that all empty squares are under attack, as has been shown here: https://puzzling.stackexchange.com/questions/107214/3-queens-and-2-rooks-covering-a-8x8-chess-board. What if we require that all squares are under attack, even those occupied by any of the fi...
The sergeant was told >!**DONT GO HOME**! --- Answers to the questions: >! ... >! 31. As a result of its shape, which variety of pasta is named after the Italian word for ‘butterfly’? **FARFALLE** >! 32. Which animal cell organelles break down macromolecules, repair cell membranes, and destroy invadi...
This question: https://puzzling.stackexchange.com/questions/107107/how-can-3-queens-control-the-white-squares got me thinking... What is the fewest number of queens needed to attack every white square? Rules: - Only queens allowed - Every white square is attacked — not just occupied - No queen attacks ano...
How many queens are needed to attack all white squares?
An Affix Riddle: - My prefix is a clue - My infix is a stutter - My suffix combines What am I?
There was an event held by a group. In this COVID19 era, there were many hardships in equipping quarantine supplies, in addition to carrying out the event. Several bottles of the same hand sanitizer were purchased for those attending the event. One bottle of the sanitizer for every ten people was equipped. One to ten p...
This might be a huge stretch, but is it: >! Jimmy Kimmel? Sweden >! [Alicia Vikander Celebrates Sweden's Midsummer Holiday with Jimmy][1] Ashton Kutcher >! Ashton played a [voice swap game on The Tonight Show][2] salmon >! Clips of the bit have been removed, but [a forum post][3] quotes a bit where...
There was an event held by a group. In this COVID-19 era, there were many hardships in equipping quarantine supplies, in addition to carrying out the event. Several bottles of the same hand sanitizer were purchased for those attending the event. One bottle of the sanitizer for every ten people was equipped. One to ten ...
This is the end result of me messing around with minecarts and moving floors. <a href="https://i.postimg.cc/ZRyZ8GJG/srb20005.png"> <img src="https://i.postimg.cc/jdYqXSwZ/srb20005.png"> </a> (Click for larger resolution. I think) When you press the red or green buttons, the neighboring platforms rotate c...
I can't find minecart puzzles like this. Do they exist?
This is the end result of me messing around with minecarts and moving floors. [![][1]][2] (Click for larger resolution) When you press the red or green buttons, the neighboring platforms rotate counterclockwise. The yellow button switches the direction of the track. The green platforms are linked. But if we...
Do minecart puzzles like this, with buttons that rotate track, exist?
There are 6 missing black pieces, and since the black pawns haven't moved, the bishop at c8 must have been captured by white knight. That gives 5 pawn captures, and so by counting, the third white knight must have promoted at g7. That means the white knight at h8 must have been there before black pawn got into g6. ...
This is the end result of me messing around with minecarts and moving floors. [![enter image description here][1]][1] When you press the red or green buttons, the neighboring platforms rotate counterclockwise. The yellow button switches the direction of the track. The green platforms are linked. But if we igno...
This is the end result of me messing around with minecarts and moving floors. [![Minecraft screenshot][1]][1] When you press the red or green buttons, the neighboring platforms rotate counterclockwise. The yellow button switches the direction of the track. The green platforms are linked. But if we ignore all o...
There are 6 missing black pieces, and since the black pawns haven't moved, the bishop at c8 must have been captured by white knight. That gives 5 pawn captures, and so by counting, the third white knight must have promoted at g7. That means the white knight at h8 must have been there before black pawn got into g6. ...
*<sup>Inspired by Avi's Vowelburger™ Riddle [here](https://puzzling.stackexchange.com/q/92931/18418)</sup>* The local Vowelburgers™ restaurant added a twist to compete its sales with the other branches. They started making double patty burgers where the patties need not be the same. To make it more interesting t...
An institute runs batches training students in C#. A new batch starts on the 1st of every month and every batch lasts for exactly 3 months (thus at any given time, the students of exactly 3 batches will be present concurrently). The table below gives the information for the total number of students studying at the inst...
<sub>This is in the spirit of the [What is a Word/Phrase™][1] series started by [JLee][2] with a special brand of [Phrase™][3] and [Word™][4] puzzles.</sub> If a word conforms to a special rule, I call it an Area Word™. Use the following examples below to find the rule. [![][5]][5] And, if you want to analy...
What is an Area Word?
>You said - **"The clock is digital, and some of the seven bars on its units digit are broken."** and then at the end you say - **"In each of these four scenarios, what is the maximum number of broken bars, and which might it/they be?"** Firstly this should mean that the answers to all the four questions sh...
<sub>This is in the spirit of the [What is a Word/Phrase™][1] series started by [JLee][2] with a special brand of [Phrase™][3] and [Word™][4] puzzles.</sub> If a word conforms to a special rule, I call it an Area Word™. Use the following examples below to find the rule. [![][5]][5] And, if you want to analy...
<sub>This is in the spirit of the [What is a Word/Phrase™][1] series started by [JLee][2] with a special brand of [Phrase™][3] and [Word™][4] puzzles.</sub> If a word conforms to a special rule, I call it an Area Word™. Use the following examples below to find the rule. | Area Words™ | Not Area Words™ | |:---...
<sub>This is in the spirit of the [What is a Word/Phrase™][1] series started by [JLee][2] with a special brand of [Phrase™][3] and [Word™][4] puzzles.</sub> If a word conforms to a special rule, I call it an Area Word™. Use the following examples below to find the rule. | Area Words™ | Not Area Words™ | |:---...
<sub>This is in the spirit of the [What is a Word/Phrase™][1] series started by [JLee][2] with a special brand of [Phrase™][3] and [Word™][4] puzzles.</sub> If a word conforms to a special rule, I call it an Area Word™. Use the following examples below to find the rule. | Area Words™ | Not Area Words™ | |:---...
<sub>*This is in the spirit of the What is a [Word™](https://puzzling.stackexchange.com/search?q=%22I+call+it%22+title%3A%22what+is%22+title%3Aword+is%3Aquestion)/[Phrase™](https://puzzling.stackexchange.com/search?q=%22I+call+it%22+title%3A%22what+is%22+title%3Aphrase+is%3Aquestion) series started by [JLee](https://pu...
I am a 7 letter word when you remove 2 letters I become short what word am I?
[![enter image description here][1]][1] [1]: https://i.stack.imgur.com/SpvOg.png Playing regular rules for both white and black try to illiminate all the squares formation by black and/or white. From the above starting setup all rooks forms a square. Also white's queen rook pawn,king knight with black's king ro...
Another riddle from ~ *Words That Get Stuck In MacGyver88's Head* ~(:P) >My prefix - ( i ) are this/these.<br><br> >My infix - The sixth lost its sixth.<br><br> >My suffix - Even though short, eating the first still leaves enough.<br><br> >My whole - A nice sight to see on a winter day's drive.<br><br> >What am ...
[![enter image description here][1]][1] Playing regular rules for both white and black try to eliminate all the square formations by black and/or white. From the above starting setup all rooks form a square. Also white's queen rook pawn, king knight with black's king rook pawn and queen knight(a2,g1,h7,b8) form the ...
<sup>An entry in [Fortnightly Topic Challenge #49: Pub Quiz Camouflage](https://puzzling.meta.stackexchange.com/questions/7159/)</sup> --- I've had the strangest day. Today I was invited to play in a chess tournament (or so I thought). As a keen (and pretty good) chess player, naturally I accepted and made my way...
What was I supposed to do?
I don't know if this is the right answer, but it seems... *plausible*? >! If you answer all the questions given, you get 16 4-letter words: >! CAGE, KYIV, IDLE, BRIE, ABLE, DIOR, HEAT, UNDO, ODIN, USSR, MONK, RHEE, TOTO, PONS, AUDI and SWAT. >! What is interesting about this is that 16 * 4 = 64 which is the nu...
What is an Area Word™?
Thank you for ordering a takeaway from Vowelburger™! Our recommended viewing for tonight is as follows: >! On Channel A = **RAM**. The [Los Angeles Rams](https://en.wikipedia.org/wiki/Los_Angeles_Rams) take on their close rivals in tonight's featured NFL game. >! >! On Channel E = **REM**. Catch up on the late...
Is it >! SNOWFLAKE? Because >! The prefix: Self explanatory, because SNOW and SNOWFLAKE are technically the same thing >! The infix: FLAK, taken away the sixth letter of the word SNOWFLAKE gives FAK, which explains the sixes, as the devils number. (If you still don't get it, it's the swearing F word. I'm no...
Is it >! SNOWFLAKE? Because >! The prefix: Self explanatory, because SNOW and SNOWFLAKE are technically the same thing >! The infix: FLAK, taken away the sixth letter of the word SNOWFLAKE gives FAK, which explains the sixes, as the devils number. (If you still don't get it, it's the swearing F word. I'm no...
Give me an R and I'll run Give me an AR and I'll come running Give me a T and I'll stop you from moving Give me a D and I'll make you move Leave me alone and I'll send you in different directions! Can you tell my name? __________ *As far as I know, this is original.*
> Stand alone > > I am someone with authority > > Add a "B" or an "H" or an "L" > > All three are synonyms Who am I?
> Stand alone > > I am someone with authority > > Add a "B" or an "H" or an "L" > All three are synonyms of each other Who am I?
<sub>This is in the spirit of the [What is a Word™/Phrase™][1] series started by [JLee][2] with a special brand of [Phrase™][3] and [Word™][4] puzzles.</sub> ----------- If a word conforms to a special rule, I call it an Eco-Friendly Word™. Use the examples below to find the rule. | Eco-Friendly Wor...
<sub>This is in the spirit of the [What is a Word™/Phrase™][1] series started by [JLee][2] with a special brand of [Phrase™][3] and [Word™][4] puzzles.</sub> ----------- If a word conforms to a special rule, I call it an Eco-Friendly Word™. Use the examples below to find the rule. | Eco-Friendly Wor...
It is well known that the eight main chess pieces cannot cover a chess board. Suppose I have two sets of the eight main pieces. What is the size of the largest chess-like square board all of whose squares can be simultaneously be attacked by one of the 16 pieces? Two bishops must occupy white cells and the other two...
It is well known that the eight main chess pieces cannot cover a chess board. Suppose I have two sets of the eight main pieces. What is the size of the largest chess-like square board all of whose squares can be simultaneously be attacked by one of the 16 pieces? Two bishops must occupy white cells, and the other tw...
It is well known that the eight main chess pieces cannot cover a chess board. Suppose I have two sets of the eight main pieces. What is the size of the largest chess-like square board all of whose squares can simultaneously be attacked by at least one of the 16 pieces? Two bishops must occupy white cells, and the ot...
I wonder if my contribution will help at all (or whether it will simply confuse more). Hopefully the former. As good, Bayesian, reasoners Alice and Bob have correctly worked out their best strategy. That is "both push". It is helpful to think of the probability space as containing 4 possibilities. Clearly if the...
I found this table, but can't seem to find any relation between the numbers. Also there is not much logic involved. | | | |------|----| | 2002 | 13 | | 1987 | 11 | | 1984 | 5 | | 1998 | 6 | | 2004 | 22 | | 1999 | 12 | | ???? | ?? | > A table with numbers. Enter the missing numbers. A lot of log...
There are 6 missing black pieces, and since the black pawns haven't moved, the bishop at c8 must have been captured by white knight. That gives 5 pawn captures, and so by counting, the third white knight must have promoted at g7. That means the white knight at h8 must have been there before black pawn got into g6. ...
I came up with this riddle today: >My Whole is of 2 terms. >My Prefix is 3 Letters. > >Term 1 is half open. >But Term 2 is mostly locked. > >My Prefix is an ex. >My Suffix is a passage. > >My infix is a symbol, >Mostly known as 32<sub>10</sub>. Feedback is appreciated. Looks like it...
Another riddle from ~ *Words That Get Stuck In MacGyver88's Head* ~(:P) >My prefix - ( i ) are this/these.<br><br> >My infix - The sixth lost its sixth.<br><br> >My suffix - Even though short, eating the first still leaves enough.<br><br> >My whole - A nice sight to see on a winter day's drive.<br><br> >What am ...
<sub>This is in the spirit of the [What is a Word™/Phrase™][1] series started by [JLee][2] with a special brand of [Phrase™][3] and [Word™][4] puzzles.</sub> ----------- If a word conforms to a special rule, I call it an F-word™. Use the examples below to find the rule. | F-words™ | Not F-words™...
There are 6 missing black pieces, and since the black pawns haven't moved, the bishop at c8 must have been captured by white knight. That gives 5 pawn captures, and so by counting, the third white knight must have promoted at g7. That means the white knight at h8 must have been there before black pawn got into g6. ...
A simple riddle from the first Harry Potter book. You are in a room with seven potions. There is a doorway ahead and a doorway behind, both engulfed in flames. Which potion will allow you to move forward to the philosopher's stone and which will let your friend back to safety? [![Potions, the dwarf is 3rd from left...
I hold the brightest of bright in a place with low light AND I am a place with low light that is not the night. What am I? Edit: The site wouldn't let me post the original version because it is not grammatically correct. I think it's better. "Both brightest of bright and place with low light; what am I?" Hi...
I was doing crossword from [NY Times, from Mon, Feb 11, 2019 by Portia Lundie / Will Shortz](https://downforacross.com/beta/play/11932) and I got the following clue. > 51 ACROSS - Times before eves, in ads The answer is "AFTS". However, I do not understand why and how "AFTS" fits the clue. Why is the answer "A...
Why is “AFTS” the solution to the crossword clue "Times before eves, in ads"?
I was doing a crossword from the [NY Times][1] (from Mon, Feb 11, 2019 by Portia Lundie / Will Shortz) and I got the following clue. > 51 ACROSS - Times before eves, in ads The answer is "AFTS". However, I do not understand why and how "AFTS" fits the clue. Why is the answer "AFTS" and how does the clue fit? ...
<sup>An entry in [Fortnightly Topic Challenge #49: Pub Quiz Camouflage](https://puzzling.meta.stackexchange.com/questions/7159/)</sup> --- Last week I popped into my local bar, Staggers, on Tuesday night with my work colleagues to have a few well drinks and jalapeño poppers, and kick some tail at bar trivia. Some...
<sup>An entry in [Fortnightly Topic Challenge #49: Pub Quiz Camouflage](https://puzzling.meta.stackexchange.com/questions/7159/)</sup> --- Last week I popped into my local bar, Staggers, on Tuesday night with my work colleagues to have a few well drinks and jalapeño poppers, and kick some tail at bar trivia. Some...
<sup>Inspired by [Avi's Vowelburger™ Riddle](https://puzzling.stackexchange.com/q/92931/18418)</sup> I ordered some Vowelburgers™ abroad, but every menu had a printing error, so the restaurant just got rid of them. Regardless, they had something for everyone, offering the normal spread plus the unconventional "W" ...
I am a nine letter word. No matter how hard you try, it is impossible to pass through. Part of me is useful to end an argument or a fight. Another part of me, in the wrong hands, can be catastrophic. You see part of me everywhere. Part of me read backwards describes criminals or crowds. Who am I?
Is it >! Bombproof? The word implies indestrutible. Cannot pass thru End an argument >!Give Proof Wrong hands catastrophic >!Bomb See part of me everywhere >!roof Reverse is criminals or crowd >!Mob
Is it >! Bombproof? The word implies indestructible. Cannot pass through End an argument >!Give Proof Wrong hands catastrophic >!Bomb See part of me everywhere >!roof Reverse is criminals or crowd >!Mob
<sup>An entry in [Fortnightly Topic Challenge #49: Pub Quiz Camouflage](https://puzzling.meta.stackexchange.com/questions/7159/)</sup> --- Last week I popped into my local bar, Staggers, on Tuesday night with my work colleagues to have a few well drinks and jalapeño poppers, and kick some tail at bar trivia. Some...
**Very partial answer** I have the answers to all the questions, and some remarks on their interpretation. Unfortunately I need to go to bed now. There is a bit of further interpretation to be worked out, and then another puzzle to solve. I expect someone else will finish the job, and I hope they will feel no guilt ...
My friend sent my this tricky puzzle... *Please explain the reason for the mistake in the number sequence - what is it trying to communicate?* 8139, 8140, 8141, 5493, 8143, 8144
> I am three, often a person, always a digit, and also without. > > George POUST was his name. > > Manufactured by Ford between 1972 and 1976. > > YMCA was not my first team in my coaching career. > > Theory of Analytical Transformations was not the last of my publications. > > The diabolical snake ruined all...
>! 323 392 645 407 713 >!After briefly checking pairs of Eisenstein integers (and even more briefly looking in horror at the Diophantine equations), I decided to force three of the five lengths to rational by iterating over integer triangles of increasing perimeter. Then, using the law of cosines and sagemath's co...
>! One solution thus far: 323,392, and 645 for the distances between points of different triangles (red), 407 and 713 for the equilaterals' edge lengths. The two triangles are rotated relative to each other by arccos(421/1147) >!After briefly checking pairs of Eisenstein integers (and even more briefly looking i...
>! One solution thus far: 323,392, and 645 for the distances between points of different triangles (red), 407 and 713 for the equilaterals' edge lengths. The two triangles are rotated relative to each other by arccos(421/1147) >!After briefly checking pairs of Eisenstein integers (and even more briefly looking i...
What is the one sound that fills the gaps?
> I am three, often a person, always a digit, and also witout. > > George POUST was his name. > > Manufactured by Ford between 1972 and 1976. > > YMCA was not my first team in my coaching career. > > Theory of Analytical Transformations was not the last of my publications. > > The diabolical snake ruined all of the loc...
My friend sent me this tricky puzzle... *Please explain the reason for the mistake in the number sequence - what is it trying to communicate?* 8139, 8140, 8141, 5493, 8143, 8144
[PARTIAL ANSWER] Solved Slitherlink: >! [![Completed Grid][1]][1] >! I've added some annotations with the numbers corresponding to the green polygons, and also shaded to further differentiate the inside and outside of the fence (in case it bears any significance. I've yet to figure out how the cipher works....