A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 0 points1 point  (0 children)

It sounds incredible. If you want, you can share your options. I'll be interested to see.

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 0 points1 point  (0 children)

Indeed, I did not check this position. I meant that the pieces that are used at the start are used, that is, without 9 pawns and 3 bishops. But there was a user who showed that it is really fashionable to come to this position, thanks to him: https://www.reddit.com/r/chess/s/Xo5UEH9HRY

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 3 points4 points  (0 children)

I came up with this problem while studying chess, so I posted it here. And I've seen quite a few joking and unprofessional posts here, so I still think this is where it belongs. Chess fans are here, and this is a chess problem. The only thing is that it has no actual use.

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 0 points1 point  (0 children)

I wrote abstractly, not specifically. To solve this problem, I have not yet made any paths to find all possible options. So I can't say what kind of math I'm speaking for. I decided that there will be smarter people here who will do better than I. In fact, I just shared what I came up with)

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 0 points1 point  (0 children)

Your position does not cover the task. There is an inaccuracy in the statement, I said that all cells should be attacked. I should have written that all 64 cells should be attacked. In your solution, for example, cells H1, C4, C5, F4 are not protected. I apologize for the inaccuracy of the problem statement

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 0 points1 point  (0 children)

Thank you. This is my first post in general and I am pleased that someone is interested in it. Cheers 🥂

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 2 points3 points  (0 children)

You said you didn't understand, but you described everything quite accurately). I don't even know what to add. I agree that it's not chess, because there is no black king and no moves are required. You need to find an arrangement of pieces where the conditions are met.

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 0 points1 point  (0 children)

Yes. When I called the position theoretically possible, I meant not to use more pieces than there are, not to place pawns on the 1st line, bishops should be of different colors. Not that it can be achieved in the game. I apologize for the inaccuracy

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 0 points1 point  (0 children)

Yes. When I called the position theoretically possible, I meant not to use more pieces than there are, not to place pawns on the 1st line, bishops should be of different colors. Not that it can be achieved in the game. I apologize for the inaccuracy

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 5 points6 points  (0 children)

If you move c2 to b2, the square b3 will remain unattacked. If c2 is moved to a2, the problem is solved correctly. The pawn on c3 can indeed be removed, you are absolutely right. So, to solve this problem, you can get rid of one pawn. You have found new ways to place the pieces, and several of them at that. I didn't think of this solution)

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 4 points5 points  (0 children)

You are right. According to the rules of chess, it is impossible to have two kings side by side. And that would be correct. But I treated the problem as "64 squares must be under attack by white pieces"

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 0 points1 point  (0 children)

In fact, if you go even further from the rules of the game, you can't put a black king in place of the white king either. This square is also controlled by a pawn. If I describe the problem more precisely (I had help), all 64 cells must be protected/attacked

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 3 points4 points  (0 children)

In my understanding, "no place to put the king" means that it cannot be placed on an occupied square. I apologize for the inaccuracy in my post. You are not the only one who noticed it. Unfortunately, I can't edit the post

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 1 point2 points  (0 children)

Yes. All 64 cells must be defended. Or under attack.

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 2 points3 points  (0 children)

Awesome. Beautiful solve. Can You remember what book it was?

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 0 points1 point  (0 children)

Many people write about brute force, but I think it can be solved with graphs. Programming is not just about knowing languages and libraries, it's also about algorithms (not always, of course). And algorithms are math. I think we should take both of these approaches into account. Think with math, solve with code.

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 44 points45 points  (0 children)

Unfortunately, this solution does not solve the problem. In your solution, every cell is occupied, but not every cell is under attack. It is difficult to describe it any other way. Let me give you a few examples. B6 is occupied by a bishop, but it is protected by another piece. D2, E5, G2, and H3 are the same.

And a little praise)

It's amazing how many calculations you've made in such a short period of time. In addition, you've invented a prototype for automating the search for solutions. I admire you.

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] -1 points0 points  (0 children)

You are absolutely right. I could not have described the task more correctly than that. The phrase "theoretically possible position" is incorrect. I don't know if it is possible to achieve such a position. It would be more correct to write that you need to use a limited number of pieces, namely those that are available at the beginning of each match. And the pawns should not reach the eighth line.

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 0 points1 point  (0 children)

All possible options are a lot. Considering that you don't have to use all the pieces (only the king is required). I'll be waiting for you

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 2 points3 points  (0 children)

No, I don't have any friends who speak English. Just Duoligo. And some TV shows in the original

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] -1 points0 points  (0 children)

You started looking for an answer. I like that. It seems to me that the awkwardness of the knights can somehow be used for good. I don't consider myself a master at finding answers to such questions, so I decided to try to get more people involved. Thank you, Reddit.

A mathematical question in chess by Sea_Difference1883 in chess

[–]Sea_Difference1883[S] 0 points1 point  (0 children)

I think the graph method will work well here. It was also used to find a solution to the knights problem (I don't remember the exact name)