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In chess, it is possible for a piece to have only one legal move. For example, in this position, the Black king can move only to h2.

enter image description here

Given that:

All 32 pieces are available for use.

Construct:

A position with as many pieces as possible that have only one legal move.

However, and this is the catch, in the event of a tie, the position that can reached the quickest, i.e. it has the shortest proof game, wins.

Now off you go! The first answer that fulfills the main question and gives proof for their tiebreaker game gets the checkmark.

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    $\begingroup$ Might be an interesting variant to do the same thing, except with king in check. $\endgroup$
    – Ben Barden
    May 12 at 21:11
  • $\begingroup$ @BenBarden I'll see to it! $\endgroup$ May 12 at 22:30
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    $\begingroup$ Also interesting: Find the shortest game where all 32 pieces have exactly 2 legal moves. $\endgroup$
    – Retudin
    May 13 at 15:20
  • $\begingroup$ @Retudin That looks like a tricky variation, I'd love to try it. $\endgroup$
    – Vepir
    May 13 at 18:00
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Here is another solution with

the full complement of 32 pieces but reachable in 12 moves and with a more interesting pawn structure:

Position:

enter image description here

Proof game:

1.e4 d5 2.e5 d4 3.h4 a5 4.g3 b6 5.f3 c6 6.Nh3 Na6 7.Be2 Bd7 8.Rf1 Rc8 9.Ng1 Nb8 10.c4 f5 11.b3 g6 12.a3 h6 *

Alternative proof game: the pawns do all the work.

Only 2 other pieces per side do actually move.
1.e4 d5 2.e5 d4 3.h4 a5 4.g3 b6 5.f3 c6 6.Rh2 Ra7 7.Be2 Bd7 8.Rf2 Rc7 9.Rf1 Rc8 10.c4 f5 11.b3 g6 12.a3 h6 *

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Vepir has helped twice in this answer, first in spotting a mistake and then with an improvement in the number of moves. Please got upvote their answer too if you like this one.

Here is a position with

All 32 pieces with exactly one move enter image description here

This position can easily be reached in

13 moves for each side (8 for each pawn, 2 for the queen and for the left bishops and 1 for the king).

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    $\begingroup$ This can be improved to one move less, if you do it on king's side instead of queen's side! $\endgroup$
    – Vepir
    May 12 at 20:49
  • $\begingroup$ @Vepir Great spot! Thank you. $\endgroup$
    – hexomino
    May 12 at 20:54
  • $\begingroup$ Does a pawn's opening move count as two possibilities? If not, this should be able to be cut down a bit more by excluding b3 and b6 for white/black respectively. $\endgroup$
    – TCooper
    May 13 at 23:16
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    $\begingroup$ @TCooper A pawn's opening move does count as two possibilities, that was my initial mistake before Vepir pointed it out to me $\endgroup$
    – hexomino
    May 14 at 8:34
  • $\begingroup$ @hexomino ah okay, too bad. Anyone else think this solution could also be a fun chess variation starting position? Pawns lose two space starting option, otherwise, play from here. At least we'd get new openings $\endgroup$
    – TCooper
    May 14 at 16:52
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Score:

Every piece has only one legal move! (21 moves to reach this position.)

Position:

enter image description here

Moves:

1. g3 b6 2. Bg2 Bb7 3. b3 g6 4. Bb2 Bg7 5. e3 d6 6. d3 e6 7. Nd2 Ne7 8. Ne2 Nd7 9. a3 h6 10. h3 a6 11. Qb1 Qb8 12. Qa2 Qa7 13. Kf1 Kf8 14. Kg1 Kg8 15. Kh2 Kh7 16. Nf1 Nc8 17. Nc1 Nf8 18. Rg1 Rg8 19. Rb1 Rb8 20. c3 f6 21. f3 c6

Fun fact,

This can start out as a real chess opening, the Hippo opening.

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I doubt this is optimal but an obvious jumping off point might be as pictured below. I believe 24 of the pieces have only one legal move (all 16 pawns, 4 rooks and 4 knights).

chess

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All solutions focus on particular pawn position... but there are others too:

All pawns have to have a single possible move. It is obvious that either pawn has to move a tile or two, OR there has to be something blocking it from moving 2 squares - say another pawn. Note that pawn's only move could be also capture (of another pawn most likely)

This means

16 moves are theoretically minimal - but there are many such options. You can see that for example one with white abcd pawns on row 5 and black efgh ones on row 4 also work at same number of moves. Piece blocking pawns is not completely impossible either, though the only solution I found was a king between 2 of his own pawns, with 2 other figures behind those 2 pawns, a space directly behind, then a pawn 2 steps behind. White's pawns remove option of moving forward.

Like this: (capital letters for black, small ones for white):

 .P.
 X.X
 PKP
 ...
 pp.

I haven't analyzed if this is actually possible or breaks at some later point. Let's forget about this one for now because I couldn't see how to use it and rather consider something else:

Let's briefly check how few moves are needed to hammer white's side only: a3 gives rook a single move and takes a square from knight. Great. It would be wonderful if b3 is played to offer bishop a tile to move. Then c pawn needs to go to 4 or 5 to not block knight, while d remains in place blocking bishop and queen. Now if we have e remaining in place too, even Q has a single c2 move. On the king side, everything is mirrored except g can go to g4/5 as well.

So, here we have partial solution (white pieces are capitalized, black are lowercase, O stands for possible position):

 RNBQKBNR
 ...PP...
 PP....OP
 ..OppOO.
 ..O..OO.
 

This requires at least

6-9 moves from white (so, 10-7 from black's pawns). If you select 8 moves each:

The following position is reached

 rnbqkbnr
 ..p..p..
 p......p
 .pP..Pp.
 ...pp...
 PP....PP
 ...PP...
 RNBQKBNR
 

This gives

26 pieces with a single move - all 16 white, 8 black pawns and 2 black rooks.

Obviously, to improve the problem is clear:

to squeeze black pieces, a lot of moves will be needed, so this probably won't be the optimal solution in terms of number of chess moves

One possible end solution is:

 qn....nr
 .b....b.
 rpp..ppk
 p......p
 ..PppP..
 PP....PP
 ...PP...
 RNBQKBNR
 

This requires

6 white moves, and 10 moves from black pawns + 2 moves from bishops, 3 moves from king, 1 move from rook and 2 moves to get queen in place.

This is in total

24 moves - 2 better than the current solution with 13 each; however, it takes 18 turns in chess due to so many moves needed from black.

As for a proof game:

1.a3,a5 2.b3,Ra6 3.c4,d5 4.f4,d4 5.g3,e5 6.h3,e4 (from now on, odd white moves are Ra2, even are Ra1. Only black moves are shown from here on). 7.Ra6 8.Qd5 9.Qa8 10.Bb7 11.c6 12.f6 13.Kf7 14.Kg6 15.h5 16.Kh6 17.g6 18.Bg7

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    $\begingroup$ Are you saying 6 white moves and 19 black moves? That is not a legal chess position (you don't have a "proof game" as required by OP's rules) since sides need to alternate their moves. But, this would be an interesting variation! (To allow non-alternating moves). $\endgroup$
    – Vepir
    May 13 at 12:46
  • $\begingroup$ @Vepir I added a sample proof game now. It should be pretty trivial to reconstruct the final position - I feel proof games are crucial only where it is not obvious how to reach the final position, while it was easy to get to the final position here. But making those moves on the board did help me to eliminate one wasteful move putting Q in place (I thought Nd7 and back but current one is faster). $\endgroup$ May 13 at 19:29
  • $\begingroup$ This is an odd variant, in which both sides are allowed to move on the same turn or not at all. An odd combo of plies form both sides! $\endgroup$ May 13 at 19:52

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