6
$\begingroup$

In chess, it is possible to double check whilst giving promotion. An example of this would be a pawn promoting to a queen while a discovered attack from a rook behind the pawn checks the opponent’s king. Both the new queen and rook check at the same time, thus making it a double check.

Construct a sequence of promotions with double check with maximal possible length. Assume that white is to move first and black is to help. You must also prove your answer to be optimal via any reasonable method.

Good luck!

Improve this question
$\endgroup$
0

2 Answers 2

Reset to default
4
$\begingroup$

I now have

Four double checks by promotion in a row.

FEN: B1nQ2B1/1P1PPP2/2k5/8/8/8/8/7K w - -

Game: 1. b8=N+ Kd6 2. dxc8=N+ Ke6 3. f8=N+ Kf6 4. e8=N+

Apronus link

Proof that it is optimal: UNDER EDIT

A double check can occur either by a classic discovery, or by an en-passant capture. The latter is impossible here so it has to be a discovery. There are three cases:

Type A: Black King in the 8th rank right in front of the pawn to be promoted, promotion = Q or R, with another Q or R in the same column as the King.

Type B: Black King in the 7th rank, checked by Rook or Queen also on the 7th rank; all four types of promotions can occur.

Type C: Black King in the 6th rank, attacking-close to the pawn to be promoted. Promotion = Q or R or N, while the other checking piece can be anything.

Now here is why there can't be too many moves:

Fact 1: there can be only one type A in the sequence. Because (long story short) the King has to leave the 8th rank and it can never come back.
Fact 2: there can be only one type B in the sequence. Because (long story short) the King has to leave the 7th rank and it can never come back.
Therefore the only possible sequences are (possibly truncated) ABCCC... and ...CCCBA.

Improve this answer
$\endgroup$
1
  • $\begingroup$ @RewanDemontay God no, I have about 10 minutes of free time per day right now, and no clue when that will change... $\endgroup$
    – Arnaud Mortier
    Commented Nov 15, 2019 at 22:45
3
$\begingroup$

I’ve managed to do

3 discovered checks, assuming that capture promotions are allowed.

The setup:

FEN: 3nnBB1/RP1kPP2/8/8/8/8/8/7K w - - 0 1

The game:

1. b8=N+ Kd6 2. exd8=R+ Ke6 3. fxe8=R+

Lichess link

I have a feeling we can do a bit better than that, but as of now this is the best I can get.

Improve this answer
$\endgroup$
2
  • $\begingroup$ I now have one more, but a proof of optimality doesn't seem easy. $\endgroup$
    – Arnaud Mortier
    Commented May 1, 2019 at 1:21
  • $\begingroup$ Really thought I had a 5, but missed the promoted piece causing a second check, and can't get around that yet. $\endgroup$
    – Joel Rondeau
    Commented May 7, 2019 at 14:23

Not the answer you're looking for? Browse other questions tagged or ask your own question.