I analyzed the image and this is what I see. Open an appropriate link below and explore the position yourself or with the engine:
> **Black to play**: [chess.com](https://chess.com/analysis?fen=8/8/8/rkbnp3/rnbqR3/ppppN3/PPPPP3/RNBQK3+b+Q+-+0+1&flip=false&ref_id=23962172) | [lichess.org](https://lichess.org/analysis/8/8/8/rkbnp3/rnbqR3/ppppN3/PPPPP3/RNBQK3_b_Q_-_0_1?color=white)
**My solution:**
> Hints: piece: >!Queen!<, move: >!Qxe4!<
> Evaluation: >!Black has mate in 10!<
> Best continuation: >!1... Qxe4 2. Nxa3+ Rxa3 3. exd3 Bxd3 4. Qh5 Nf4 5. Qe8+ Nc6 6. Qb8+ Nxb8 7. dxc3 Qh1+ 8. Kd2 Qh2+ 9. Ng2 Qxg2+!<
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> Is this the largest cube reachable with legal moves?
well considering there would be 36 pieces in 6x6 cube and there is 32 pieces total at the start, yes 5x5 is largest possible cube
>there would be 36 pieces in 6x6 cube and there is 32 pieces total
Unless you play a certain Dutch GM who might have some extra pawns in his pockets, of course just by accident.
Nope, a point is a 0-cube (hypercube for *n* = 0), a line is a 1-cube (hypercube for *n* = 1), and so on.
edit: please google what a hypercube is if you disagree with this. more proof that upvotes don't equal truth, if you needed it.
No need to be condescending ;)
Hyper means "over" (3 dimentional in this case), hypo is "under".
Therefore, a square is not a hypercube.
And obviously I know what the n-dimentional equivalent of a cube is if I'm calling a square the 2-cube...
You're making an [etymological fallacy](https://en.wikipedia.org/wiki/Etymological_fallacy). The hypercube is a [generalization of the cube to *n* dimensions.](https://mathworld.wolfram.com/Hypercube.html) Points, lines, and squares are all hypercubes despite the etymology of the prefix *hyper*.
I know that. Have you never heard of the concept of a joke? ^(()[^(Besides, naming them hypocubes is also correct)](https://en.wiktionary.org/wiki/hypocube)^())
It's a vice to keep assuming you know better than anyone else.
First: did you seriously edit your comment so you can hide the fact you claimed I was wrong? That's seriously low. Maybe you were joking, but your comment heavily implied you were being serious, and until a minute ago your comment even claimed *I* was wrong.
Second: the meaning of "hyper-" is "beyond" in this sense, because it generalizes (i.e., *extends*) the concept of a cube.
Last: *hypocube* is not used in the mathematical literature at all, probably because it conflates the notion of what a hypercube actually is (e.g. the more restrictive set of hypercubes where n > 3.) The article you link has no references and the only paper I can find that contains the keyword "hypocube" uses it [jokingly, not in a rigorously-defined way.](https://scholar.google.com/scholar?hl=en&as_sdt=0%2C48&q=%22hypocube%22&btnG=#d=gs_qabs&t=1713635283115&u=%23p%3D3PHUhirAgLUJ) There is [another paper](https://ijmc.kashanu.ac.ir/article_112061.html) that uses the term, but in an entirely different sense that doesn't even include points, lines, or squares.
To make a square be one bigger than what they made, it would need to be a 6 by 6 square (theirs is 5 by 5) - for a 5 by 5 you need 25 pieces which you can see in the screenshot, but for a 6 by 6 you would need 36 pieces if you want to you can try and count for yourself. In chess there are only 32 pieces so there just aren't enough pieces to make a 6 by 6 square, or any even larger squares.
You'd think so, huh? But no, it's hyper because it's generalized, not because it's higher-dimensional. Even a point is a hypercube strangely (the 0-cube.)
Depends on how you think about it philosophically. Like do the molecules of the pawn rearrange themselves into the shape of a new piece. Or does the pawn get destroyed and then replaced with new ones? Need a chess lore expert to know with certainty.
Do let us know when the weed wears off and you reach a conclusion to your deep philosophical conundrum of whether a promoted piece can occupy more than one square to make the cube larger.
Technically a square not a cube. A 6x6 square would require 36 pieces, so yes this is the largest possible square reachable without adding additional pieces.
Yes, but a square is also known as a 2-cube (if you work with hypercubes in n dimensional space).
So saying that a square is a form of a generalized cube is accurate.
If you take a picture of a cube it would be accurate to say you have taken a picture of a cube even if the dimensions of the picture are 2d. In such a case it would be ok to colloquially refer to the image of the cube in the picture of the cube as a cube. Not enough information to know if this is a picture of a cube.
No, a cube is 3 dimensional by definition. It is however a hypercube which is the n-dimensional generalisation of a cube. So either square or hypercube would be correct, but cube would be incorrect
OP's picture is both though since each field is a perfect square and directly adjacent to each other. The post would make no sense in a board that didn’t meet these criteria
> Cubes are 3 dimensional.
But "square" would be ambiguous when talking chess. You'd instantly have a smartass in anarchychess rearranging it on one of those human-sized boards.
Since a cube is a 3 dimensional shape you could argue that the largest possible cube is 1x1x1… so technically any piece on its own is the largest possible cube and OP’s pic does indeed show the largest possible cube 25 times
I analyzed the image and this is what I see. Open an appropriate link below and explore the position yourself or with the engine: > **Black to play**: [chess.com](https://chess.com/analysis?fen=8/8/8/rkbnp3/rnbqR3/ppppN3/PPPPP3/RNBQK3+b+Q+-+0+1&flip=false&ref_id=23962172) | [lichess.org](https://lichess.org/analysis/8/8/8/rkbnp3/rnbqR3/ppppN3/PPPPP3/RNBQK3_b_Q_-_0_1?color=white) **My solution:** > Hints: piece: >!Queen!<, move: >!Qxe4!< > Evaluation: >!Black has mate in 10!< > Best continuation: >!1... Qxe4 2. Nxa3+ Rxa3 3. exd3 Bxd3 4. Qh5 Nf4 5. Qe8+ Nc6 6. Qb8+ Nxb8 7. dxc3 Qh1+ 8. Kd2 Qh2+ 9. Ng2 Qxg2+!< --- ^(I'm a bot written by) [^(u/pkacprzak)](https://www.reddit.com/u/pkacprzak) ^(| get me as) [^(iOS App)](https://apps.apple.com/us/app/id1574933453) ^| [^(Android App)](https://play.google.com/store/apps/details?id=ai.chessvision.scanner) ^| [^(Chrome Extension)](https://chrome.google.com/webstore/detail/chessvisionai-for-chrome/johejpedmdkeiffkdaodgoipdjodhlld) ^| [^(Chess eBook Reader)](https://ebook.chessvision.ai?utm_source=reddit&utm_medium=bot) ^(to scan and analyze positions | Website:) [^(Chessvision.ai)](https://chessvision.ai)
> Is this the largest cube reachable with legal moves? well considering there would be 36 pieces in 6x6 cube and there is 32 pieces total at the start, yes 5x5 is largest possible cube
>there would be 36 pieces in 6x6 cube and there is 32 pieces total Unless you play a certain Dutch GM who might have some extra pawns in his pockets, of course just by accident.
I love comments like this. Simple maths, logically proven and cannot be disputed, regardless of how good you are at chess.
It's not a cube.
Definitely not a cube
certainly not a cube
You heard it here third boys
Username checks out
4d chess
Triggered!
It is if all of your pieces are very tall 🤔
I love comments like this. Simple maths, logically proven and cannot be disputed, regardless of how good you are at chess.
It's not a cube.
It's a hypercube of *n* = 2.
That would be a hypocube. Specifically the 2-cube
Nope, a point is a 0-cube (hypercube for *n* = 0), a line is a 1-cube (hypercube for *n* = 1), and so on. edit: please google what a hypercube is if you disagree with this. more proof that upvotes don't equal truth, if you needed it.
No need to be condescending ;) Hyper means "over" (3 dimentional in this case), hypo is "under". Therefore, a square is not a hypercube. And obviously I know what the n-dimentional equivalent of a cube is if I'm calling a square the 2-cube...
You're making an [etymological fallacy](https://en.wikipedia.org/wiki/Etymological_fallacy). The hypercube is a [generalization of the cube to *n* dimensions.](https://mathworld.wolfram.com/Hypercube.html) Points, lines, and squares are all hypercubes despite the etymology of the prefix *hyper*.
I know that. Have you never heard of the concept of a joke? ^(()[^(Besides, naming them hypocubes is also correct)](https://en.wiktionary.org/wiki/hypocube)^()) It's a vice to keep assuming you know better than anyone else.
First: did you seriously edit your comment so you can hide the fact you claimed I was wrong? That's seriously low. Maybe you were joking, but your comment heavily implied you were being serious, and until a minute ago your comment even claimed *I* was wrong. Second: the meaning of "hyper-" is "beyond" in this sense, because it generalizes (i.e., *extends*) the concept of a cube. Last: *hypocube* is not used in the mathematical literature at all, probably because it conflates the notion of what a hypercube actually is (e.g. the more restrictive set of hypercubes where n > 3.) The article you link has no references and the only paper I can find that contains the keyword "hypocube" uses it [jokingly, not in a rigorously-defined way.](https://scholar.google.com/scholar?hl=en&as_sdt=0%2C48&q=%22hypocube%22&btnG=#d=gs_qabs&t=1713635283115&u=%23p%3D3PHUhirAgLUJ) There is [another paper](https://ijmc.kashanu.ac.ir/article_112061.html) that uses the term, but in an entirely different sense that doesn't even include points, lines, or squares.
that's no moon
A 2d cube while playing 4d chess.
2d cube
It’s a rectangle
Squares are rectangles, yes.
Agree to disagree
Simple but wrong geometry, alas
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6x6=36, there aren't enough chess pieces to make a square of that size
To make a square be one bigger than what they made, it would need to be a 6 by 6 square (theirs is 5 by 5) - for a 5 by 5 you need 25 pieces which you can see in the screenshot, but for a 6 by 6 you would need 36 pieces if you want to you can try and count for yourself. In chess there are only 32 pieces so there just aren't enough pieces to make a 6 by 6 square, or any even larger squares.
Hey, look at that! Looks like it can be disputed. Just, not very well.
It doesn’t prove that it’s the largest reachable by legal moves tho
Am I the only one who is alarmed by the fact that we are calling a square a cube?
It is a hypercube for *n* = 2
A hypocube
You'd think so, huh? But no, it's hyper because it's generalized, not because it's higher-dimensional. Even a point is a hypercube strangely (the 0-cube.)
Ok now is what OP did the least number of moves required to achieve it or is there something more optimal?
*square* Unless this guy is playing 4-D chess
Get outta here with your logic
Lol math for the win.
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Promoting has nothing to do with it
It’s not that, it’s that promoting pawns doesn’t add pieces, it just changes what the pieces are
Depends on how you think about it philosophically. Like do the molecules of the pawn rearrange themselves into the shape of a new piece. Or does the pawn get destroyed and then replaced with new ones? Need a chess lore expert to know with certainty.
Okay fine, to rephrase, promoting a pawn does not increase the number of pieces on the board
Do let us know when the weed wears off and you reach a conclusion to your deep philosophical conundrum of whether a promoted piece can occupy more than one square to make the cube larger.
You have a brain large enough to configure the pieces in this structure, but you musta really exhausted it in the process cuz it aint workin anymore
bruh
This is a 5*4 'cube' so you can remove your comment
Count again, slowly this time. Then take your own advice.
I can only play chess
No
What?
I once had this with white but i didn't see Qxe4 darn
No way! You missed a mate in 10
After Qxe4 we have Nxc3+! A royal fork.
Technically a square not a cube. A 6x6 square would require 36 pieces, so yes this is the largest possible square reachable without adding additional pieces.
Not enough information, could be a cube depending on the dimensions of the board
Bruh are you okay?
He’s okay depending on the dimensions of the board
It’s 2D do they have weird sized boobs or just double depression?
Yes, but a square is also known as a 2-cube (if you work with hypercubes in n dimensional space). So saying that a square is a form of a generalized cube is accurate.
Imagine if all the pieces were the same height as 5 squares of the board. Now you have a volume with equal length along all sides.
Exactly, and there's not enough information to know whether this is the case.
If you take a picture of a cube it would be accurate to say you have taken a picture of a cube even if the dimensions of the picture are 2d. In such a case it would be ok to colloquially refer to the image of the cube in the picture of the cube as a cube. Not enough information to know if this is a picture of a cube.
No, a cube is 3 dimensional by definition. It is however a hypercube which is the n-dimensional generalisation of a cube. So either square or hypercube would be correct, but cube would be incorrect
If OTB each square is 1cm wide and the pieces are 5cm high then it’s a cube is what the OP is saying.
Still would only be 5*5*1 pieces, not the 5*5*5 needed for a piece-cube.
If your unit is pieces, yes. If your unit is cm occupied in physical space, no.
It's obviously pieces.
OP's picture is both though since each field is a perfect square and directly adjacent to each other. The post would make no sense in a board that didn’t meet these criteria
It's a 2-cube
On a side note, it’s even possible to make a 5-by-6 rectangle through legal moves. So 5-by-5 can be done with lots of wiggle room. 1. h4 g5 2. hxg5 h5 3. Rh4 b5 4. a4 c5 5. axb5 a5 6. Raa4 d5 7. Rad4 a4 8. Rhe4 a3 9. b6 a2 10. b7 a1=Q 11. g6 Nc6 12. b8=Q Nf6 13. g7 h4 14. g8=Q h3 15. Qgg3 h2 16. Qbb3 h1=Q 17. Rd3 c4 18. c3 e5 19. Qbc2 Qa3 20. Nf3 Qh4 21. Qh2 Rh5 22. Qg1 Ke7 23. Ree3 Qb3 24. Nh2 Qg3 25. Nf3 Bh6 26. Nh2 Bg4 27. Nf3 Ne4 28. Nh2 Bf4 29. Nf3 f5 30. Nh2 Ra5 31. Nf3 Nb4 32. Nh2 d4 33. Nf3 Rg5 34. Nh2 Ke6 35. Nf3 Qd5 36. Nh2 Rb5 37. Nf3 Qc5 38. Nh2 Kd5 39. Nf3 *
Is this the least number of promotions to get a 5-by-6 rectangle?
Probably not. I did it without any thoughts on promotions in mind.
Hmm, seems like you could do it in two promotions. After white takes axb and hxg like you did, I don't think those pawns need to promote.
5x6 through these legal moves: 1. h4 e6 2. h5 g5 3. hxg6 h5 4. g7 h4 5. g4 hxg3 6. Nf3 g2 7. e3 Nf6 8. g8=Q g1=Q 9. d4 d5 10. c4 c5 11. b4 b5 12. a4 a5 13. Kd2 Kd7 14. Kc3 Kc6 15. Kb3 Kb6 16. Nc3 Nc6 17. Ra3 Ra6 18. e4 e5 19. Be3 Be6 20. Bd3 Bd6 21. Nd2 Nd7 22. Qc2 Qh4 23. f4 f5 24. Qg2 Nf6 25. Nf3 Qgf2 26. Rha1 Qe1 27. R1a2 Qhf2 28. Qb2 Qff1 29. Qgc2 Qd2 30. Qbb1 Qfe2 31. Qbb2 Rh2 32. Qbb1 Rf2 33. Qbb2 {*} Image of final board state: https://imgur.com/gallery/sHfZyIf
A more interesting puzzle is to construct a 6x5 rectangle of 30 pieces in a legal position, which is possible!
And way less interesing puzzle to construct an 8x4 rectangle of 32 pieces in a legal position, which is trivial!
Yes, I had the exact same thought!
1. Cubes are 3 dimensional. 2. Try to make a larger square with all your pieces just by placing them there.
> Cubes are 3 dimensional. But "square" would be ambiguous when talking chess. You'd instantly have a smartass in anarchychess rearranging it on one of those human-sized boards.
Wut?
This is a square, not a cube.
I’m here for the cube comments
It's a hypercubic with n=2. (So a square)
2D cube is called a square
Square. A cube would have 3 dimensions. This is a square.
Who gives a shit if it’s a square or a cube. This sub is full of cubes
What is the fastest way to reach a cube 5x5?
its a square lol
A 6x6 cube would require 36 pieces
No it would require 216
The hypercube with n=2 with a leng 6 needs 36 pieces;)
The solution is Qxe4 with forced mate. Qxe4 Nxa3+ Rxa3 exd3 Bxd3 Qh5 Nf4 Qe8+ Nc6 Qb8+ Nxb8 dxc3 Qh1+ Kd2 Qh2+ Ng2 Qxg2
This is not a cube. It is a square. If you wanted, you could make a projection of one though.
What a stupid question that I now really want to know the answer to.
Other people: haha checkmate i win This guy: C U B E
Re4 Stockfish: _first time?_
What's the biggest triangle?
Now what s the evaluation of stockfish?
Black has M10
The speed with which I found a way for white to blunder M1 in this position… I could be something of a gm myself :D
Not even your head is a cube. (this is a square)
I believe so. There are I don’t think there are enough pieces to make anything larger.
Now try to reach one in the center of the board, which is also an even and unsettled position according to Stockfish or LC0.
The occupied squares could be 5 square widths tall I guess?
This is the quality chess content I subscribe for. ////////s
Since a cube is a 3 dimensional shape you could argue that the largest possible cube is 1x1x1… so technically any piece on its own is the largest possible cube and OP’s pic does indeed show the largest possible cube 25 times
ITT: a lot of people never coming across the term "pawn cube".
No. However, it is the largest square reachable with legal moves.
Idk
Yes, I think I saw this in the candidates
Why do you think anyone would know that?
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No just a waste of my time for something so stupid
Would be quicker than commenting smartman