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        riddles >> medium >> Putting All Your Pawns in a Row
        
(Message started by: Quetzycoatl on Jan 5^th, 2004, 11:29am)

Title: Putting All Your Pawns in a Row
Post by Quetzycoatl on Jan 5^th, 2004, 11:29am

Assuming you have the cooperation of your opponent, but still abiding all the rules of Chess:

What is the greatest number of your pawns you get into one column at any one time?

What is the greatest number of yours and your opponents pawns that can end up in two columns?

Title: Re: Putting All Your Pawns in a Row
Post by Barukh on Jan 6^th, 2004, 5:27am

on 01/05/04 at 11:29:56, Quetzycoatl wrote:

Assuming you have the cooperation of your opponent, but still abiding all the rules of Chess:

What is the greatest number of your pawns you get into one column at any one time?

Theoretically, it's 6 (no pawn is on the first line; no pawn is on the last line), and it can be done quite easily [hide]make it on the "d" line, sacrifying 11 black pieces and a couple of white pieces[/hide].

Title: Re: Putting All Your Pawns in a Row
Post by THUDandBLUNDER on Jan 6^th, 2004, 6:12am

Quote:

and it can be done quite easily

For the first part, 9 captures are required - not so difficult.

But 6 pawns on the rook's file requires 15 captures.
That's probably not so easy to arrange.

Title: Re: Putting All Your Pawns in a Row
Post by Barukh on Jan 7^th, 2004, 1:16am

on 01/06/04 at 06:12:42, THUDandBLUNDER wrote:

For the first part, 9 captures are required - not so difficult.

You are right, I don’t know why I thought it’s 11. :-/

Quote:

But 6 pawns on the rook's file requires 15 captures.
That's probably not so easy to arrange.

Is it possible? What is wrong with the following argument (assuming pawns arrange at the “a” column)
[smiley=blacksquare.gif][hide]
1. All black pieces – except the king, obviously – must be captured.
2. All the captures (of black pieces) take place in the triangular area e3-a3-a7.
3. At every square in this area, exactly one capture happens.
4. To be captured, black pawns f7, g7, h7 must capture at least 8 white pieces.
5. White pawns g, h cannot be captured; so there are not enough white pieces to be sacrified.
[/hide][smiley=blacksquare.gif]

Title: Re: Putting All Your Pawns in a Row
Post by THUDandBLUNDER on Jan 7^th, 2004, 4:14am

Quote:

What is wrong with the following argument

Barukh, I agree with your analysis - as far as it goes.

However, the Black king-side pawns can promote to another piece and then sacrifice themselves.

Quetzalcoatl's second puzzle seems more difficult.

Title: Re: Putting All Your Pawns in a Row
Post by rmsgrey on Jan 8^th, 2004, 7:21am

Also, the black h-pawn can capture the white g-pawn as one of the 8 captures