From: davewood@bruno.cs.colorado.edu (David Rex Wood)
Subject: Re: Sextupled pawns Re: Quadruple pawns 
Keywords: sextupled a-pawns!?
Organization: University of Colorado, Boulder
Date: Thu, 28 Jan 1993 22:25:56 GMT

In article <1993Jan28.221646.27266@colorado.edu> davewood@bruno.cs.colorado.edu (David Rex Wood) writes:
>In article <1993Jan26.224738.19839@husc3.harvard.edu> elkies@ramanujan.harvard.edu (Noam Elkies) writes:
>>In article <1993Jan26.054608.2373@noose.ecn.purdue.edu>
>>achar@ecn.purdue.edu writes:
>>>Another one of those "once in a while" games.
>>>[Amusing ICS games with quadrupled Black e-pawns omitted]
>>
>>...which reminds me:
>>
>>White: Ke1, Ra1, pawns a2,a3,a4,a5,a6,a7
>>Black: Ka8
>>
>>k _ . _ . _ . _
>>P . _ . _ . _ .
>>P _ . _ . _ . _
>>P . _ . _ . _ .
>>P _ . _ . _ . _
>>P . _ . _ . _ .
>>P _ . _ . _ . _
>>R . _ . K . _ .
>>
>>Two puzzles:
>>
>>i. (easy) White to play and mate in 8.
>>
>>ii. (considerably harder) is the position, and the solution, legal?
>>[That is, could this arise by legal --- albeit ridiculous --- play
>>from the initial position?]
>>
>>--Noam D. Elkies (elkies@zariski.harvard.edu)
>>  Dept. of Mathematics, Harvard University
>
>
>-- 
>-------------------------------------------------------------------------------
>David Rex Wood -- davewood@cs.colorado.edu -- University of Colorado at Boulder
>-------------------------------------------------------------------------------

Strange, my response disappeared.  Lets try this again...

In article <1993Jan26.224738.19839@husc3.harvard.edu> elkies@ramanujan.harvard.edu (Noam Elkies) writes:
>In article <1993Jan26.054608.2373@noose.ecn.purdue.edu>
>achar@ecn.purdue.edu writes:
>>Another one of those "once in a while" games.
>>[Amusing ICS games with quadrupled Black e-pawns omitted]
>
>...which reminds me:
>
>White: Ke1, Ra1, pawns a2,a3,a4,a5,a6,a7
>Black: Ka8
>
>k _ . _ . _ . _
>P . _ . _ . _ .
>P _ . _ . _ . _
>P . _ . _ . _ .
>P _ . _ . _ . _
>P . _ . _ . _ .
>P _ . _ . _ . _
>R . _ . K . _ .
>
>Two puzzles:
>
>i. (easy) White to play and mate in 8.
>
>ii. (considerably harder) is the position, and the solution, legal?
>[That is, could this arise by legal --- albeit ridiculous --- play
>from the initial position?]
>
>--Noam D. Elkies (elkies@zariski.harvard.edu)
>  Dept. of Mathematics, Harvard University

Okay, I sat through a couple classes not paying attention and playing with
number ii.  Here is (I think) the optimal solution...


First, YES, it can be done.
The are 15 (5+4+3+2+1) required pawn captures for white which corresponds
to the number of pieces black has to lose.  Further important is the fact
that white has 9 pieces to waste.  At some point, each of black's 15 pieces
needs to move to the lower left side of the board, like this:

K-------
B-------
BB------
BBB-----
BBBB----
BBBBB---
--------
--------  (Where B is a black piece, K is black's king)

To make this work we can either promote 3 of black's pawns (easy solution) or
promote only one and move the other two across diagonally.  This is what I
did and solved the problem in 39 moves.  I think this is optimal based on
the following:

Piece		Number of moves to get to a place it can be captured
------------------------------------------------------------
a pawn		1 (to make life easier on QR)
b-e pawns	1+1+2+3 = 7
f pawn		5 (=Q) +2 = 7
g,h pawns	4 (captures) each = 8
QR		1
QN		1
QB		2 (doing it in 1 conflicts with QN)
Q		2 (doing it in 1 conflicts with a-pawn, b-pawn, or h-pawn)
K		4
KB		1
KN		3
KR		2

So, while it is conceivable (loosely) that we could knock off 4 more moves
for black (a pawn, QB, Q and K (could castle)) all of these would cause
other numbers to increase.  I'm pretty sure 39 is as good as it gets.

To make sure I wasn't cheating, I played it through.  This is certainly not
the only solution and its not even all that pretty -- but it works.

1. g4  a5
2. g5  Ra7
3. g6  hxg6
4. Bh3  Na6
5. Bf5  gxf5
6. Nc3  b6
7. Ne4  fxe4
8. Nf3  Nf6
9. Ne5  Nd5
10. Nd3  exd3
11. exd3  e5
12. Qf3  e4
13. Qf6  gxf6
14. h4  Ba3
15. bxa3  c5
16. Bb2  e3
17. Be5  fxe5
18. Rb1  f5
19. Rb3  Ndb4
20. h5  Rxh5
21. Rh4  f4
22. Rc3  f3
23. Rd4  exd4
24. fxe3  dxc3
25. dxc3  d5
26. cxb4  d4
27. bxa5  Qd5
28. exd4  Qb3
29. dxc5  Be6
30. cxb6  Bc4
31. cxb3  f2+
32. Kd2  Rb5
33. dxc4  f1Q
34. cxb5  Kd8
35. bxa6  Qf4
36. Kd1  Qa4
37. Ke1  Kc8
38. bxa4  Kb8
39. bxa7+  Ka8
-- 
-------------------------------------------------------------------------------
David Rex Wood -- davewood@cs.colorado.edu -- University of Colorado at Boulder
-------------------------------------------------------------------------------