Chess/Math Puzzle: A Topological Approach

In summary, the conversation is about a chess/math puzzle invented by JZI. The puzzle involves coming up with a condition or new rule in which black wins without either side making any moves. The conversation includes various ideas and solutions proposed by different individuals, such as identifying opposite edges, using a Moebius strip, and playing on a torus or cylinder. Ultimately, the solution is for any piece on a black square to be captured, resulting in a win for black.
  • #1
janzizka
8
0
This is a chess/math puzzle I invented:

Consider a fully set up chess board (in starting position).

Invent a condition (new rule) in which black wins without either side making any moves.

Note: this problem has a really abstract and *topological* approach. :rofl:

Please email me the solution (sophiek@brandeis.edu), or any questions/comments.

JZ
 
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  • #2
I hope you post the solution here soon too.
 
  • #3
Perhaps you should go into a little more depth about the content of the condition? I can think of a bunch of possible solutions off the top of my head, so a little clarification would help.
 
  • #4
the condition is on the board, not the pieces (or moves).

I also have a spoiler, but I am more interested to hear your ideas without a give away.
 
  • #5
Im a little confused though about exactly what I can do... I mean can I have a conditino like the board is slanted so the king falls off nd this signifies check mate? this can be done so only the white king falls...

Your conditions are still too general. Maybe you could come up with some more clarification...?
 
  • #6
I am not considering the application of any physical forces (such as gravity)
 
  • #7
Yes, there are several possible solutions, and none that we come up with is likely what you have in mind.

Here's one : If any of the squares in the first two rows from the end are vacant, the player on that side loses (white plays first).

This condition is "on the board" and ensures that white loses, but is probably not what you want.
 
  • #8
janzizka said:
Invent a condition (new rule) in which black wins without either side making any moves.
This is still too vague !

identify opposite edges : white is mate.
 
  • #9
It works also with a Moebius strip :tongue2:
 
  • #10
OK, I guess that would be double mate ?
So identify the opposite edges without right to going through it on your turn ? A "virtual identification".
 
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  • #11
Inspired from Gokul : if any among rows 3 and 4 are not empty (5 and 6 for black) the corresponding king is mate
 
  • #12
Any king sitting on an odd row is mate
 
  • #13
humanino...it seems you are quite the expert on mating ! :wink:
 
  • #14
New Chess Rule: If you are black you win automatically at the start of a chess game
 
  • #15
Tom McCurdy said:
New Chess Rule: If you are black you win automatically at the start of a chess game
You cheated ! No rule on the pieces ! Only rules one the board. Well, that is not more silly than what I wrote anyway :rofl:
 
  • #16
I think the thing you may be thinking of is if the chess board was connected by the other end... kind of like an old video game where you go out one side and come in the other side. You allow the pieces to move backwards to the other end of the board and since white moves first white is in checkmate... although its really more of stale mate since both pieces with be in checkmate ... (roughed out... sorry it is late.
 
  • #17
Here is another one : any player either touching a pieche sitting on a prime number row, or making any piece sitting on a prime number row looses the game.
 
  • #18
ah, but the game must be over before you touch the pieces
 
  • #19
ok, I cheated :smile:
 
  • #20
Tom McCurdy said:
I think the thing you may be thinking of is if the chess board was connected by the other end... kind of like an old video game where you go out one side and come in the other side. You allow the pieces to move backwards to the other end of the board and since white moves first white is in checkmate... although its really more of stale mate since both pieces with be in checkmate ... (roughed out... sorry it is late.

I like this (though it begs some questions about 'what happened before') !

PS : I'm almost positive this is the correct answer as this makes the chessboard behave like a projective plane - and that's the "topological" thingy involved in it.
 
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  • #21
White assumes normal starting position. Black assumes normal starting position with the following exceptions: queen's knight starting position is d3, king's knight starting position is f3.
 
  • #22
Tom McCurdy said:
I think the thing you may be thinking of is if the chess board was connected by the other end... kind of like an old video game where you go out one side and come in the other side. You allow the pieces to move backwards to the other end of the board and since white moves first white is in checkmate... although its really more of stale mate since both pieces with be in checkmate ... (roughed out... sorry it is late.

Actually at the moment the game officially begins, white could stop the clock and tell the referee that his adverdary has made an illegal move because his King would be next to his own King. The referee agrees and white wins. :smile:
 
  • #23
Tom McCurdy's reply was actually what I had in mind, though it is easier to phrase it as a chess game on a torus.
The solution with the mobius strip works as well.
It's true that both sides will be in checkmate, but in chess the first side which cannot move loses, and since white must go first, black wins.
 
  • #24
quasar987 said:
Actually at the moment the game officially begins, white could stop the clock and tell the referee that his adverdary has made an illegal move because his King would be next to his own King. The referee agrees and white wins. :smile:

That's true, and I hadn't thought of that.
But black hasn't exactly made an "illegal" move because it hasn't made any move at all, the board is just not set up correctly for playing on a torus.
 
  • #25
actually playing on a mobius strip or a cylinder would work too :)
 
  • #26
Any piece on a black square is captured.

Game over white.


And I used the board, too.
 

1. What is a topological approach to solving chess/math puzzles?

A topological approach is a method of solving a chess/math puzzle by using principles and concepts from the field of topology, which is a branch of mathematics that studies the properties of geometric shapes and spaces.

2. Can anyone use a topological approach to solve these puzzles?

Yes, anyone with a basic understanding of topology can use this approach to solve chess/math puzzles. However, some puzzles may require a deeper knowledge of topology and mathematics in general.

3. How does topology help in solving chess/math puzzles?

Topology helps in solving these puzzles by providing a different perspective and approach to the problem. It allows for the use of techniques such as mapping, folding, and stretching to manipulate the puzzle and find a solution.

4. Are there any benefits to using a topological approach?

Yes, using a topological approach can help in developing critical thinking and problem-solving skills. It also allows for a more creative and unique solution to the puzzle.

5. Are there any limitations to using a topological approach?

While topology can be a useful tool in solving chess/math puzzles, it may not always be the most efficient or practical approach. Some puzzles may have simpler solutions using other methods or may not require the use of topology at all.

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