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Here’s a fun one! I call it Pawninos because the pawns, like dominos, all fall into a cycle!

Start with an 8x8 chess board. Give black his king on h4 and no other material. Give white all of his 8 pawns and his king, and nothing else. Put all available white pieces on their original squares. This is a legal position because knights can swoop past pawn lines.

With white to move first, and black to help, construct a game to check black 44 times or more (if possible) in a row in a legal sequence of moves. A PGN post shall be needed for an accepted answer.

A Stipulation: Promted pieces may not move after promotion.

You must also prove this optimal via any reasonable method.

Good luck!

UPDATE: Also try to go for promotion checks ONLY after all possible non-promotion checks have run out. Again, the number is 44 or more here. This is a second category, not change of rules.

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  • $\begingroup$ Did you add a new rule that promotion checks can only happen after all non-promotion checks? $\endgroup$
    – noedne
    Commented Apr 29, 2019 at 23:57
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    $\begingroup$ As a matter of etiquette, I think it's a little bit off to add a second part to your puzzle after the original puzzle has been solved. Put yourself in the shoes of the person who solves the original: perhaps they found a clearly-best solution to your puzzle and went to bed, secure in the knowledge that they'd nailed it. Then you add a second part, and suddenly their solution isn't a complete solution any more; maybe someone else comes along and solves the second part and they're left looking as if they couldn't do it. If I were noedne I'd be a little bit annoyed here. $\endgroup$
    – Gareth McCaughan ♦
    Commented Apr 30, 2019 at 1:21
  • $\begingroup$ Has a correct answer been given? If so, please don't forget to $\color{green}{\checkmark \small\text{Accept}}$ it :) $\endgroup$
    – Rubio ♦
    Commented May 7, 2019 at 4:58
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    $\begingroup$ (You added the second half of the question over an hour after posting—almost half an hour after noedne had posted an essentially full answer to the question as originally posted, 17 minutes after that answer was slightly expanded upon to its current form, and basically simultaneously with the addition of a Lichess link at your request. It's... a little disingenuous to now assert that the first answer only addressed half the question, and thus does not deserve acceptance for being incomplete.) $\endgroup$
    – Rubio ♦
    Commented May 8, 2019 at 0:42

2 Answers 2

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The maximum is

48 checks.

PGN:

[FEN "8/8/8/8/7k/8/PPPPPPPP/4K3 w KQkq -"] 1. g3+ Kg4 2. h3+ Kf5 3. g4+ Kg5 4. h4+ Kf4 5. e3+ Ke4 6. f3+ Kd5 7. e4+ Ke5 8. f4+ Kd4 9. c3+ Kc4 10. d3+ Kb5 11. c4+ Kc5 12. d4+ Kb4 13. a3+ Ka4 14. b3+ Ka5 15. b4+ Kb6 16. c5+ Kb5 17. a4+ Ka6 18. b5+ Kb7 19. c6+ Kb6 20. a5+ Kc7 21. b6+ Kd6 22. e5+ Ke6 23. d5+ Ke7 24. d6+ Kf7 25. e6+ Kf6 26. g5+ Kg6 27. h5+ Kg7 28. h6+ Kg6 29. f5+ Kh7 30. g6+ Kg8 31. h7+ Kg7 32. h8=B+ Kxh8 33. g7+ Kh7 34. g8=B+ Kg7 35. f6+ Kxg8 36. f7+ Kg7 37. f8=B+ Kxf8 38. e7+ Kf7 39. e8=B+ Kxe8 40. d7+ Ke7 41. d8=B+ Kxd8 42. c7+ Kd7 43. c8=B+ Kxc8 44. b7+ Kc7 45. b8=B+ Kb7 46. a6+ Kxb8 47. a7+ Kb7 48. a8=Q+ Kxa8

Lichess: https://lichess.org/RP8jbdgO

Proof of optimality:

48 is the maximum number of moves allowed by the rules.

Basic idea:

Pushing the pawns one rank at a time at the start is straightforward. To set up the bishop promotion chain at the end, it is helpful to keep the f-pawn behind the g- and h-pawns to avoid interfering.

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Answer to second part of question

Here's a 46 in the "second category": all pawn checks before any promotions. I don't think there's any particular need for spoiler markup here; it's not as if a casual glance at what follows will reveal much.

[FEN "8/8/8/8/7k/8/PPPPPPPP/4K3 w KQkq -"]

1. g3+ Kg4 2. h3+ Kf5 3. g4+ Kg5 4. h4+ Kf4
5. e3+ Ke4 6. f3+ Ke5 7. f4+ Ke4 8. d3+ Kd5
9. e4+ Kc5 10. d4+ Kb4 11. a3+ Kc4 12. b3+ Kb5
13. a4+ Kb4 14. c3+ Ka5 15. b4+ Kb6 16. a5+ Kb5
17. c4+ Kc6 18. b5+ Kd6 19. c5+ Ke6 20. d5+ Kf6
21. e5+ Kg6 22. h5+ Kh6 23. g5+ Kg7 24. h6+ Kg6
25. f5+ Kf7 26. g6+ Ke7 27. f6+ Kd7 28. e6+ Kc7
29. d6+ Kb7 30. a6+ Ka7 31. b6+ Kb8 32. a7+ Kb7
33. c6+ Kc8 34. b7+ Kd8 35. c7+ Ke8 36. d7+ Kf8
37. e7+ Kg8 38. f7+ Kh8 39. g7+ Kh7 40. g8=B+ Kxh6
41. f8=B+ Kh5 42. e8=B+ Kh4 43. d8=B+ Kh3 44. c8=B+ Kh2
45. b8=B+ Kh1 46. a8=B+

And here's a playable lichess link showing those moves.

It's pretty easy to see that you can't get 48 checks with this restriction. Proof: If you do then after the first 40 checks white's pawns must be on a7...h7. The last move was a check so the BK is somewhere on the 8th rank. And now his next move must be to capture a pawn, which means that that pawn can never give a "promotion-check". So, at most 47.

Is 47 possible? Well, it seems like there are two cases. 40 pawn checks and 7 promotion-checks; or 39 pawn checks and 8 promotion-checks. In the second case, if the "missing" pawn check isn't the very first pawn move then the pawns don't all promote and therefore we can't get 8 promotion-checks. I am fairly sure that any position you can achieve by making the first pawn move not be a check can equally well be achieved by making it be a check (and don't propose to prove this in detail; it's kinda obvious). So actually only the first case matters.

If there are 40 pawn checks then, as above, we must end up with white's pawns all the way across the 7th rank and black in check. In order not to be in check from two pawns simultaneously (obviously impossible) the BK must be in a corner, so WLOG the BK is at h8 and the last move was g7+. What was black's move before that? Kh8, obviously, but from where? Not from h7 because there's a white pawn there, so from either g7 or g8. On g8, the BK would have been in check from the f- and h- pawns simultaneously, which is impossible. So the BK came from g7. That is, we had: (BK at g7, WPs on a7-f7,g6,h7) Kh8; g7+. But then the BK on g7 wasn't in check, which won't do.

So, 47 is impossible too and 46 (as above) is best possible with the pawn-checks-first restriction.

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  • $\begingroup$ Retracted since in fact it turns out we can do two more and someone else has done it. $\endgroup$
    – Gareth McCaughan ♦
    Commented Apr 29, 2019 at 23:30
  • $\begingroup$ I unretracted it because it is a better "second-category" solution than noedne's (which isn't trying to be a "second-category" solution since you added that bit of the question after they posted their solution). $\endgroup$
    – Gareth McCaughan ♦
    Commented Apr 30, 2019 at 0:00
  • $\begingroup$ I will. But I'm not sure I haven't goofed, so I won't transcribe it yet. $\endgroup$
    – Gareth McCaughan ♦
    Commented Apr 30, 2019 at 0:06
  • $\begingroup$ Yeah, I have goofed: some of those moves are illegal. I do have a different working 46-mover but I want to see whether I can do more (in the "second category"). $\endgroup$
    – Gareth McCaughan ♦
    Commented Apr 30, 2019 at 0:07
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    $\begingroup$ @GarethMcCaughan In Lichess you can promote the variation you want to keep until it is the main one, then delete the alternative variations. $\endgroup$
    – noedne
    Commented Apr 30, 2019 at 0:57

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