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I had a chess position today, in which my last position had 5 possible moves to checkmate. This seemed like a lot to me, and I immediately thought of the puzzle: Which position would yield the maximum number of ways to checkmate the opponent on the next move?

The rules of my made up puzzle are thus

  1. Exactly 1 King per side
  2. Any amount of any other kinds of pieces are allowed for either side
  3. "Score" for the position is the number of winning moves there are

I came up with the following position. By my count, this has 70 total winning moves. I wonder what the maximum would be?

enter image description here

Follow up puzzles which occurred to me:

  1. What's the fewest number of pieces for which every legal move would be checkmate?
    • Pawns aren't allowed
    • Exactly 1 King per side
    • White to move. All black pieces are counted in the answer
    • Alternate rule: you can only have one kind of piece, so there's a unique answer for each kind of piece
  2. What's the fewest number of points for which every legal move would be checkmate?
    • Pawns aren't allowed
    • Exactly 1 King per side
    • White to move. All black pieces' points are counted in the answer
    • Q=9,R=5,B=3,N=3,K=3

Anyone have any suggested solutions to the above puzzles?

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  • $\begingroup$ There are way too many questions in one here. The "main question" feels like it's probably a duplicate, but the follow-up questions seem nice. $\endgroup$
    – Bass
    Apr 29, 2021 at 21:47
  • $\begingroup$ Hmm, maybe it's not an exact dupe, the earlier question requires a mate from a reachable position. It has an answer with 105 checkmates. $\endgroup$
    – Bass
    Apr 29, 2021 at 21:59
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    $\begingroup$ Does this answer your question? Highest number of mates $\endgroup$
    – Sleafar
    Apr 29, 2021 at 22:03

2 Answers 2

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Unless I'm misunderstanding the rules, you can easily construct cheap forced mates by

putting white in check: (4 non-Kings, 16 14 points)
enter image description here

And along the same lines, some single-piece boards:

three queens or rooks, five bishops, or five knights should do the trick:
enter image description here

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  • $\begingroup$ Good one. I hadn't considered putting the opposing side in check to force a capture as the only legal move. This is probably (close to?) the optimal solution for the additional puzzles. Perhaps I should've made a separate puzzle Q for each sub-puzzle. $\endgroup$ Apr 29, 2021 at 20:21
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So many questions in one. Here's my answer to the follow-up question(s):

3 pieces, 13 points:

Which can be achieved like this:

enter image description here

White's only legal move is Kxb3#.

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