Minimum N moves

I've been trying to look at this, and haven't as yet solved it, though have managed some working out. Hope to resume again this evening. Thus far I've got a bit of the problem.

White has made six pawn captures (five from c2 to h7 and exf3). They can't be either B so must be seven from h-pawn, 2xN, 2xR, Q and promoted a-pawn.

Therefore black has made four pawn captures (fxg6, cxd6 and two by the a-pawn). These must be Q, 2xN and B(from f1). The B on c1 can't have moved before capture.

The white k must have made the 8th rank via b6 and c7, the rooks via the f-file. A bit of shuffling round for the K (f7, f8, d8) to get them in. The black K must be there too beforehand as he has to have made h8 before his f-pawn captures and hence also before a P arrives at h7.

So a black piece (specifically a N) must have blocked g8.

White has moved last (black could have no legal move), quite possibly to take the aforementioned N. Quickest way of doing that would be for it to move g8-f6-d5-f4-e6(with check)-f8(blocking discovered check). That's five moves.

The other black N needs three moves minimum to get onto any of d3, e4, f5 or g6.

The white N on b1 can move to either a3 or c3 and be captured by the a-pawn (which has first captured, possibly a B on b5). One move.

The second N has to move to either d6 or g6, the minimum there is three moves (g1-h3-f4-g6).

That's 12 in total. I think I'm on the right track, but not completely happy with it yet. Usually miss something, will try and look again a bit later.

Originally posted by SwissGambit
Yeah. Your schedule's already booked for solving the math problems on here.

But no worries. I post these kind of problems occasionally to see if there are any others who enjoy them. If that's not you, don't sweat it.

Edit: Hey! Aren't you the guy who said, "The whole point of a mathematical proof is its VIGOUR!" Same applies to retros!

touché

😳

This is far to hard for me!

Originally posted by Peakite
I've been trying to look at this, and haven't as yet solved it, though have managed some working out. Hope to resume again this evening. Thus far I've got a bit of the problem.

White has made six pawn captures (five from c2 to h7 and exf3). They can't be either B so must be seven from h-pawn, 2xN, 2xR, Q and promoted a-pawn.

Therefore black has made fo ...[text shortened]... mpletely happy with it yet. Usually miss something, will try and look again a bit later.

If you try to retract a few moves, it will bring further enlightenment [frustration?]

Originally posted by SwissGambit
[fen]2bRRK1k/1p1pp1pP/3p2p1/P6P/8/5P2/1P1P1PP1/8[/fen]

What is the minimum number of N moves required to legally reach this position?

I don't think this position is possible unless the pawn on g6 is on f6 instead

Originally posted by preachingforjesus
I don't think this position is possible unless the pawn on g6 is on f6 instead

I'd be very surprised if this position weren't legal, Swiss Gambit is pretty good with his problems.

Still thinking....

Thus far,

The captures are as above, but white has made one which could be on any square. The rooks must have gone via f7.

If black were to retract f7xg6 then the white piece captured can retract any move and black has no legitimate last move. White can't have played exf3 as a final move as his B would have blocked from becoming a balck capture.

Must have been -1 Kf7xNf8 (nothing else could have been there) Nd6-f8

Now I don't seem to have any more uncaptures left until f7xg6 can be reversed, and need to get the rooks in, shielded by the wK and bN.

Five moves back (all by N for black), gives:



The a/h pawns give up to six possible white retractions at some point, they don't prevent anything else from happening (blacks a-pawn promoted on c1).

Stuck here at the moment.

That leaves far too many moves for the K/R whilst the N waits.

Originally posted by Peakite
I'd be very surprised if this position weren't legal, Swiss Gambit is pretty good with his problems.

Still thinking....

Thus far,

The captures are as above, but white has made one which could be on any square. The rooks must have gone via f7.

If black were to retract f7xg6 then the white piece captured can retract any move and black has no legiti ...[text shortened]... Stuck here at the moment.

That leaves far too many moves for the K/R whilst the N waits.

You just showed why the Ng8 idea won't work. Black has nothing to do while White evacuates the Rooks. You'll need a different plan that gives Black something to do at that point.

Originally posted by preachingforjesus
I don't think this position is possible unless the pawn on g6 is on f6 instead

It is indeed a legal position, but the proof is not obvious.

Originally posted by preachingforjesus
I don't think this position is possible unless the pawn on g6 is on f6 instead

no, I explained earlier how the rook and king got to where they are...
but again:
King goes from c7-d8-e8-f7 after Black has played fxg7
then the rook come in on the h-file after all the necessary pieces are out of the way.
meaning it's possible, just a matter of counting moves, or using logical analysis, as most have/are doing.

Originally posted by rubberjaw30
no, I explained earlier how the rook and king got to where they are...
but again:
King goes from c7-d8-e8-f7 after Black has played fxg7
then the rook come in on the h-file after all the necessary pieces are out of the way.
meaning it's possible, just a matter of counting moves, or using logical analysis, as most have/are doing.

Getting a rook in on the h-file is going to prove very difficult. There has been a pawn of one color or another on h7 the whole game.

Key question: What other piece can shield on g8, besides a black Knight?

Originally posted by SwissGambit
Key question: What other piece can shield on g8, besides a black Knight?

OK, so here's the problem. I need two pieces reborn: a piece to shield on g8, and a BLACK piece to move around while White extracts Rooks. The reason bNg8 won't work is that I can't just uncapture two Black pieces in a row.

Why? Because, after the necessary -1.Kf7xNf8, just to give Black something to retract, all the remaining missing pieces were captured by pawns. White may not uncapture with Ph7 until Pg6 goes back, and Pf3 waits for Bf1 to return home. And the uncaptured bN has to unpromote before it can uncapture any White pieces.

Therefore, by elimination, a WHITE unit must shield on g8. Candidates: wN, or wB. Now that I've narrowed it down to a 50/50 choice, can anyone guess which one it is?

After deciding it isn't a black N, really could only be one of the two. However as it must be captured the pawn. Just figured which pawn, yet not quite how.

The bN must retract back to c1 (4 moves) whilst white retracts his a pawn then h pawn (I'll say this way round as that still allows chance for a wR to move out after exf3 is retracted).

Blacks pawn uncaptures on c2 and possibly b3.

Inclination is on a wB at the moment. A wN seems unlikely as it would take longer to reach g8.

Edit: Lets make it a wN. Unravelling coming up:

-1. Kf7xNf8 Ne6-f8
-2. Kf8-f7 Nd4-e6
-3. a4-a5 Nb3-d4
-4. a3-a4 Nc1-b3 (c1 as it's quicker to get a wB back to f1 from c2 rather than a2)
-5. a2-a3 c2-c1=N

It would be helpful to get another black piece into play ASAP, the pawn only has 5 possible moves left to retract. Even with a wB quickly to g8 I can't see enough moves to get the rooks out without another black piece to move. It can't be an uncapture from the h7 pawn, so must be on f3. Therefore I need to get the wB back to f1.

-6. h5-h4 b3xBc2 (can't now move the h4 P back until wR gets back to h1)

It must therefore be the wN on g8 as no black pieces are available until another uncapture and I can only have a wN, Q or R uncaptured as blacks pawn retreats. To minimise N moves, must be uncaptured on b4 or b6 to give a minimum 3 moves back to g8.

-7. Bd3-c2 b4-b3
-8. Bf1-d3 a5xNb4 (uncapture now as otherwise W will be retro-stalemated with nothing to move after d2xf3)

Now blacks a-pawn can't be retracted until the R gets back to a7/a8.

-9. e2xRf3 Rb3-f3+ (it's at this point when I think blacks moves don't actually matter too much, plently of variety available without moving a N).
-10. Nd5-b4 Rb6-b3
-11. Nf6-d5 Ra6-b6
-12. Ng8-f6 Ra7-a6