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This is the second part of Fastest way to helpmate

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You have been given the task to checkmate/helpmate black in fastest possible way in following ways:

  1. Pawn promoting to only queen
  2. Pawn promoting to only knight
  3. Pawn promoting to only bishop
  4. Pawn promoting to only rook
  5. No pawn promotion allowed

Your score is the sum of moves required to checkmate in all the cases above. The lowest score wins.

FEN: 2bnnbr1/2prkqp1/2ppppp1/8/8/K7/6P1/8

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  • $\begingroup$ Possible [no-computers] tag ? Because if computers are used it would be a lot easier. $\endgroup$
    – Varun W.
    Commented May 24, 2022 at 22:12
  • $\begingroup$ Here is one good site: lichess.org/analysis/2bnnbr1/2prkqp1/2ppppp1/8/8/K7/6P1/… $\endgroup$
    – JLee
    Commented May 25, 2022 at 0:28
  • $\begingroup$ Let us continue this discussion in chat. $\endgroup$
    – bobble
    Commented May 25, 2022 at 1:29
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    $\begingroup$ The conclusion from the discussion seems that this puzzle might produce a widely enough accepted answer to still be on topic, even if it's beaten later on, so should be on-topic. $\endgroup$
    – PuzzlingFerret
    Commented May 25, 2022 at 14:16
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    $\begingroup$ @I'm Nobody yep, or that your target audience would rather do something other than puzzling, such as play chess. :) $\endgroup$
    – JLee
    Commented May 28, 2022 at 15:56

2 Answers 2

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Shaved it down to 32 total moves.

Can this be beaten?

It wouldn't surprise me a bit.

  1. Queen (6-move)

1. g4 Nb7 2. g5 Rd8 3. gxf6+ Kd7 4. fxg7 Nf6 5. gxf8=Q Ne8 6. Qxf7#

  1. Knight (6-move)

1. g4 g5 2. Kb3 Qh5 3. gxh5 Nf7 4. h6 Rd8 5. h7 Bd7 6. hxg8=N#

  1. Bishop (7-move)

1. g4 f5 2. gxf5 Nb7 3. fxg6 Rd8 4. gxf7 Kd7 5. fxg8=B Be7 6. Bh7 e5 7. Bf5#

  1. Rook (6-move)

1. g4 Nb7 2. g5 Rd8 3. gxf6+ Kd7 4. fxg7 Nf6 5. gxf8=R Ne8 6. Rxf7#

  1. No pawn promotion (7-move)

1. g4 f5 2. Kb3 Kf6 3. Kc3 Be7 4. Kd3 Bf8 5. Ke3 Be7 6. Kf4 Bb7 7. g5#

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  • $\begingroup$ 4 of them are definitely optimal. I just have doubts over case "without promotion". I will put efforts, If I don't find a shorter solution, I will give it a checkmark. $\endgroup$
    – I'm Nobody
    Commented May 29, 2022 at 6:52
  • $\begingroup$ @I'm Nobody The king is just so far from the pawn, and the king must guard the pawn for the mate, so they must come together. Also, the K being surrounded by strong pieces tends to negate the pawn. I wonder if there's a way to program an engine to find these types of collaborative mates. $\endgroup$
    – JLee
    Commented May 29, 2022 at 11:20
  • $\begingroup$ It actually exists to my surprise, however you cannot tweak it to find mates with conditions. helpman.komtera.lt $\endgroup$
    – I'm Nobody
    Commented May 29, 2022 at 13:40
  • $\begingroup$ @I'm Nobody Wow cool! I didn't know it existed either. $\endgroup$
    – JLee
    Commented May 29, 2022 at 14:32
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Minor Addendum: Time to invoke some more loophole abuse, just for fun! The question does not explicitly state whose move it is. Also, traditionally, in helpmates, Black starts first. Thus, I think, the score is best expressed as the total number of White moves; which, at the moment, is a total of 31.

I invoke this mainly because the crux (read: whole) of my answer relies on it.

Seeing as how there aint't no rule against computers, and given that I am a chess composer who is aware of chess software, I went to my go-to helpmate solver, the Helpmate Analyzer--I'm glad to see that it has been found by others in the comments above/below.

After running the position through, we can down the score to 31.

The engine finds a unique helpmate in five, which is the only possible solution in fives moves, that involves knight promotion:

1.g5 g4 2.Qh5 gxh5 3.Nf7 h6 4.Rd8 h7 5.Bd7 hxg8=N#

This has the additional effect of verifying that 6 moves is indeed optimal for queen and rook promotion. The jury is still out on bishop promotion; although 7 moves seems optimal since there is no evidence, as of yet, against it.

For non-promotion, however, I can conjure up a weak proof of optimality. The king must walk over to support the pawn to give mate. Given the distance, the king is forced to walk 4 or 5 squares, in which the pawn must complement 1 or 2 moves. Intuition tells me that the pawn must move to f3, f4, f5, g4, or g3 for a potentially shorter mate, given the above math. However, Black can neither block off the king's escape squares and/or unprotect the mating squares in time. Thus, 7 moves is optimal for non-promotion.

And there we have it, a score of 31 with some proof attached.

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  • $\begingroup$ I'm excited to see it, but your coordinates are wacky. It is white to move first. Also, A1 is on the bottom left, and H8 is at the top right. Lastly, what is S, is it a Knight? I have always seen the knight as N, since the K for king is already taken. $\endgroup$
    – JLee
    Commented May 29, 2022 at 23:23
  • $\begingroup$ @JLee The question does not explicitly state which side is to move. Therefore, I invoke loophole abuse once more. I've fixed the knight letter (S is German, the helpmate software was chosen to display an S instead of an N)., but coordinates are just fine. $\endgroup$
    – Rewan Demontay
    Commented May 30, 2022 at 0:36
  • $\begingroup$ Isn't the FEN part of the puzzle? And if it wasn't the OP's intention for white to move first, don't you think he would have mentioned it when responding to my answer? $\endgroup$
    – JLee
    Commented May 30, 2022 at 0:38
  • $\begingroup$ @JLee The OP, from all the comments I see, has not stated that Black cannot move first; thus, it is allowed. he FEN represents the position yes, but it is as only as accurate as the information the puzzle pertains to it. Every way to Sunday, my answer is valid. $\endgroup$
    – Rewan Demontay
    Commented May 30, 2022 at 0:54
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    $\begingroup$ I'm quite surprised, not a single user pointed out, which side has to move first. You're right, I cannot declare your answer wrong either. Also as @JLee said I had my intention for white to move first opposed to traditional black $\endgroup$
    – I'm Nobody
    Commented May 30, 2022 at 8:19

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