Chess/Math Puzzle: A Topological Approach

[janzizka]

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.

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

JZ

 

[quasar987]

I hope you post the solution here soon too.

 

[nolachrymose]

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.

 

[janzizka]

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.

 

[T@P]

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...?

 

[janzizka]

I am not considering the application of any physical forces (such as gravity)

 

[Gokul43201]

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.

 

[humanino]

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.

 

[humanino]

It works also with a Moebius strip

 

[humanino]

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".

 

[humanino]

Inspired from Gokul : if any among rows 3 and 4 are not empty (5 and 6 for black) the corresponding king is mate

 

[humanino]

Any king sitting on an odd row is mate

 

[Gokul43201]

humanino...it seems you are quite the expert on mating !

 

[Tom McCurdy]

New Chess Rule: If you are black you win automatically at the start of a chess game

 

[humanino]

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

 

[Tom McCurdy]

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.

 

[humanino]

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.

 

[Tom McCurdy]

ah, but the game must be over before you touch the pieces

 

[humanino]

ok, I cheated

 

[Gokul43201]

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.

 

[Chronos]

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.

 

[quasar987]

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.

 

[janzizka]

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.

 

[janzizka]

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.

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.

 

[T@P]

actually playing on a mobius strip or a cylinder would work too :)

 

[Alkatran]

Any piece on a black square is captured.

Game over white.


And I used the board, too.