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I've thought of a few different ways a chess game could go on moving only pawns, but I've only counted moves in one scenario:

  1. Both White and Black take 16 moves to line their pawns at the middle of the board.
  2. With a series of orderly captures in 8 moves, White and Black each wind up with 4 pawns each.
  3. Taking care to threaten the rooks first, White and Black move their pawns within striking distance of the opponent's non-pawn pieces. This would take 16 moves (bringing the total up to 40), except that...
  4. As soon as a White pawn threatens the Black king, Black would be forced to move the queen, a bishop or a knight to protect the king.

Have I thought through this scenario correctly? And even if I have, might could there be a scenario in which moving something other than a pawn could be put off longer?

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It seems like we can extend your scenario for a little while longer by delaying central pawn movements (which will check the king) in favor of edge pawn movements (which will capture the major pieces). –  Eric Stucky Jul 2 at 2:49
1  
In point 3, each player only has for pawns left, so only eight moves to get to the seventh rank. –  Ross Millikan Jul 2 at 3:13
    
There is a puzzling stackexchange too. I'm uncertain whether this would be a better fit there or not. –  mixedmath Jul 2 at 22:29
1  
@mixedmath Or maybe there's a chess stackexchange, too. I think this is the stackexchange with just the right degree of Sheldonian thoroughness to uncover the right answer regardless of whatever arithmetical or logical mistakes I might make in posing the question. –  Robert Soupe Jul 3 at 1:13
    
There is a chess stack exchange, but I think puzzling is the proper place for this question. Certainly there are some chessplayers that would be interested, but it is closer to the interest here. Unfortunately, puzzling has much less activity than math. I posted to meta.stackexchange supporting cross posting for cases like this. –  Ross Millikan Jul 3 at 4:44

2 Answers 2

Edit: This is an improved version of my previous 39-move solution (using Ross Millikan's suggestion to let the pawns advance as far as possible befrore being captured).

  1. c3 b6
  2. c4 b5
  3. c5 b4
  4. c6 b3
  5. g3 e6
  6. g4 e5
  7. g5 e4
  8. g6 e3
  9. axb3 dxc6
  10. fxe3 hxg6
  11. h3 a6
  12. h4 a5
  13. h5 a4
  14. h6 a3
  15. h7 a2
  16. hxg8N axb1N
  17. b4 g5
  18. b5 g4
  19. b6 g3
  20. b7 g2
  21. bxa8N gxh1N
  22. b3 g6
  23. b4 g5
  24. b5 g4
  25. b6 g3
  26. b7 g2
  27. bxc8N gxf1N
  28. e4 c5
  29. e5 c4
  30. e6 c3
  31. e7 c2
  32. exf8N cxd1N
  33. e3 c6
  34. e4 c5
  35. e5 c4
  36. e6 c3
  37. e7 c2
  38. d3 f6
  39. d4 f5
  40. d5 f4
  41. d6 f3
  42. exd8N f2+
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You can do better by having pawns move more before being captured.

1-4 b2-b6 g7-g3 5 hg ab 6-9 g3-g7 b6-b2 10 g7xh8N b2xa1N 11-15 g2-g7 b7-b2 16 g7xf8N b2xc1N 17-21 a2-a7 h7-h2 22 a7xb8N h2xg1N 23-26 e2-e6 c7-c3 27 dc fe 28-31 c3-c7 e6-e2 32 c7xd8N e2xd1N 33-37 c2-c7 e7-e2 38 f2 e2xf1N 39-42 f3-f7+ d7-d3

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@bof: good points. I believe I have fixed them. I flipped the white and black pawns in the second batch to fix the retake on f8, so I believe 43 is correct. For confirmation, each player has $8$ pawns that can make $6$ moves each, for $48$ We lose two for each pawn that gets captured and one for the White f pawn that doesn't get to advance to the eighth rank, leaving $43$. Thanks much. –  Ross Millikan Jul 3 at 4:43
    
By "b7-b" on moves 11-15, you mean "b7-b2"; by "c7-e3" on moves 23-26 you mean "c7-c3". Unfortunately, 38.c7xb8N is impossible because of 22.a7xb8N. –  bof Jul 3 at 5:06
    
You get to 43 White moves if you assume that 5 white pawns reach the 8th rank. The pawn captures 5 hg ab and 27 dc fe leave 3 white pawns on the a & c files. If they aren't going to capture any more black pawns, and the black pieces aren't going to move out of the way, those 3 white pawns can only promote on the 2 black swquares b8 & d8. So one of White's queenside pawns is going to be stalled on the 7th rank, as well as the f pawn which will give check at f7. –  bof Jul 3 at 5:57
    
@bof: I see how your flipping gets the last check to be on the black side. Good on you –  Ross Millikan Jul 3 at 13:25

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