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Today, we had the great privilege to see @Paul Panzer's answer being ticked at @thesilican's absorbing puzzle.

I here propose a variant of his puzzle where it's not mandatory to use a legal chess game.

Provide a checkerboard with as many chess pieces you want where:

  • It is Black's turn to move
  • Black is in check
  • Black has the greatest number of different legal moves possible
  • "As many chess pieces you want..." except that there will be exactly one Black King!

In the following non legal chess game because there is an extra black Queen as well as there is no white King, you can uncheck Blacks with 12 different moves, moving a black Queen to e2, e3 and e4 or by moving the King.

enter image description here

It is possible to do 42 thanks to Paul Panzer's answer but how much can you get with non legal games?

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I believe the optimum is 68. e.g. 8 pawn, 26 knight and 34 queen moves.

fill the a and e column with knights, the b and d column with queens. Then place a white rook on c1, the king on c8, and replace b2 and d2 with pawns, for "Pauls extended solution"

enter image description here

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  • $\begingroup$ @BenBarden I dont think so, I believe yours is: In "The queens on 2 and 8 have two unchecking moves each (4x4)" ; this should be 4*2. $\endgroup$ – Retudin Nov 27 '20 at 16:21
  • $\begingroup$ Bah. Right you are. Fixed, and thank you. $\endgroup$ – Ben Barden Nov 27 '20 at 16:31
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There should be a single white piece. We need to put the king in check (requiring a white piece) but we want to make it as easy as possible to get back out again (so any other white pieces are either superfluous or actively detrimental).

We're trying to maximize how many ways there are to break the check. That means moving the king, getting between the king and the offending piece, or eliminating the offending piece. A trivial consideration will determine that the white piece should not be a knight or a pawn, as they don't allow the range necessary for truly large numbers of blocks.

There's no reason to include any black pieces other than knights, queens, and the one king. We're trying to maximize the number of black options, and all other pieces have strictly fewer options than a queen.

The king's ability to move can be safely ignored. Any space that he might move to other than directly away from the threat could instead be filled by a unit that would have at least one blocking move, and directly way from the threat will not save him anyway.

Further, the king and the threat should be as far away from one another as possible, as this maximizes the number of squares that one could interrupt

Having the attack be a straight rather than a diagonal is preferred. Both allow the same number of squares to interrupt (either by blocking or by killing the target) but the straight allows more pieces on either side of both the king and the threat.

and thus...

The optimal configuration is a broad avenue. Black King at e1, white rook at e8, columns d and f filled entirely with black queens, and columns c and g filled entirely with black knights. The knights on rows 1, 2, and 8 have 1 unchecking move each (6x1), as do the queens on 1 (2x1). The queens on 2 and 8 have two unchecking moves each (4x2), as do all other knights (10x2). All other queens have three unchecking moves (10x3). Total unchecking moves is 66

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  • $\begingroup$ Could you provide a picture of your answer's setup? $\endgroup$ – bobble Nov 27 '20 at 16:25
  • $\begingroup$ @bobble I cannot. If someone else wishes to edit such a thing in, though, I would welcome it. $\endgroup$ – Ben Barden Nov 27 '20 at 16:29
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The existing modification of the original answer seems quite solid. So I thought I would give it a go with

a check via bishop move

The best I could get for this was:

56
enter image description here
The breakdown by piece is:
38 by knight, 12 by bishop and 4 by rook
Try it online

User wimi pointed out an improvement

If you replace f7 and g6 with rooks you get an extra 2, bringing it up to 58.
enter image description here
The breakdown by piece is:
20 by knight, 12 by bishop and 26 by rook
Try it online

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    $\begingroup$ If I am not mistaken, the knights on g6 and f7 can be replaced by rooks, adding 2 moves. $\endgroup$ – wimi Dec 9 '20 at 12:41
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    $\begingroup$ @wimi Yes you are right. I will update this shortly. $\endgroup$ – Sriotchilism O'Zaic Dec 9 '20 at 13:22

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