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 23:18:45 GMT

In article <1993Jan28.231209.29679@colorado.edu> davewood@bruno.cs.colorado.edu (David Rex Wood) writes:
>In article <1993Jan28.222556.27575@colorado.edu> davewood@bruno.cs.colorado.edu (David Rex Wood) writes:
>>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
>>-------------------------------------------------------------------------------
>
>
>-- 
>-------------------------------------------------------------------------------
>David Rex Wood -- davewood@cs.colorado.edu -- University of Colorado at Boulder
>-------------------------------------------------------------------------------

Again, my post disappeared...here is the new stuff I added...

----
Arrg.  I just looked at this again and I did cheat.  I didn't see the white
rook.  This means 2 black pawns must be promoted which adds 3 moves,
giving a total of 42.

Its not nearly as fun this way though.  Oh well.

Here is a solution to that problem...

1. g4  a5
2. g5  Ra7
3. g6  Na6
4. Nf3  hxg6
5. Nc3  b6
6. Ne4  d5
7. Nh4  e5
8. Nf5  Ba3
9. bxa3  gxf5
10. Bh3  fxe4
11. Rg1  f5
12. Rg3  f4
13. Rd3  exd3
14. exd3  e4
15. Qh5  e3
16. fxe3  d4
17. exd4  c5
18. dxc5  Rxh5
19. cxb6  Nf6
20. Bd7  Bxd7
21. Bb2  Ba4
22. Bc3  Rb5
23. h4  Ne4
24. Ke2  g5
25. Ke1  gxh4
26. Ke2  Qd5
27. Ke1  Qb3
28. cxb3  f3
29. bxa4  Nxc3
30. dxc3  h3
31. Kd2  f2
32. Kd1  f1Q
33. Kd2  Qf4
34. Kd1  Qb4
35. cxb4  h2
36. bxa5  h1Q
37. Kd2  Qd5
38. Ke1  Qc4
39. dxc4  Kd8
40. cxb5  Kc8
41. bxa6  Kb8
42. bxa7  Ka8
-- 
-------------------------------------------------------------------------------
David Rex Wood -- davewood@cs.colorado.edu -- University of Colorado at Boulder
-------------------------------------------------------------------------------
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