Fairy

Daniel's word on retrograde analysis in Growing Men

Chess is a domain where, as for many others, the access to beauty is open to all but requires a phase of initiation sometimes important.
In the case of fairy chess that the Master popularizes since more than 30 years, for each new genre approached he always took care to present first "elementary" problems perfectly didactic even if they could be without interest for the expert.

So far, nothing but the obvious in what I have said. They describe the classic situation of "face-to-face" courses where the speaker has all the leisure to adapt his speech to the level of the listeners present in the room.
The problem is complicated in this new course given in videoconference and directly published on this site. The problem is complicated in this new course given in video conference and directly published on this site. The occasional walker will always be able to find his way in the "classical" chess (at the price of more or less efforts).
On the other hand, the enchantment part, to remain interesting, must be adapted to the level of the reader (or at least compatible with). The Master has therefore chosen problems that are accessible to the usual audience (if not findable by them!). This is found in the now classic "the Master's diagrams" section.
Alas, inevitably, Turnbull's very pure and admirable problem will only discourage, if not sicken, the uninformed reader. This would be as much a pity for the false idea he will have of fairyland as it would be for himself, who would thus miss the opportunity to discover the full interest of the genre and even, dare I say it, its accessibility!"

I will therefore take advantage of this textual part offered to the clerk's freedom to try to make this problem accessible to the possible willing and curious reader who would not have been able to take advantage of the indispensable phases of initiation of which I spoke above.

Enlarging chess: from the moment a piece has played a move, it can no longer play a move of lesser length. Thus, it can then play moves of the same or greater length, knowing that as soon as it plays a move of greater length, this becomes the new base measure below which moves are no longer allowed.

Of course, since legal moves here are more than elsewhere conditioned by the past, it is easy to imagine that backward analysis will not be absent.

Simplified principles of retrograde analysis:

Rule 1)Any information about the past that can be proven can (and should) be used.

Rule 2)Any move whose illegality cannot be proven is presumed legal. Or: that which cannot be shown to be prohibited is permitted.

Illustrations in Growing Men :

B: Kh1 N: Be4. Black to move. what blacks plays ?

Point 1) Since this position is given Black to move, we deduce that Kh1 is not in check.
This means that Fe4 is not allowed to make Bxh1 and therefore his previous move had a length of more than 3 steps of B.
His only legal move is therefore Fa8, which now checks.

Point 2)If RB has arrived at h1 via g2, then he is doomed to play moves of length 1.4 (root of 2 to be precise since it is a move traversing the diagonal of a square of side 1. In this case, everyone knows that the diagonal is longer than the side).
And then the Ns can announce mate by playing Ba8 because they attack the squares h1 and g2 and the wK is not allowed to play at g1 or h2 since these moves would be shorter than his previous move.
For all that, the Bs are not matched because the position does not allow to prove that they did not get to h1 by g1 or h2.

To summarize: in point 1, according to rule 1, we prove that Ba8 is the only move, so it must be played.
In point 2, according to rule 2, we cannot forbid KKg1 or Kh2, one of them can (and even must in the circumstances) be played.

Now let us turn to the choice piece, namely the problem itself.
R. Turnbull

Growing Men. W's play and mate in 6 moves.

A) Let's consider bP h2.
The presence of bP h7 shows that this pawn h2 is not the Ph. So it comes from one of the files (from c to g, whatever) knowing that it made at least one capture at one point (to change file) and that from that point on, all its moves were only captures, the normal march moves having become illegal as too short.
All this to conclude that he necessarily passed through g3!
In the wake of this, we have the following reflection: which piece played the last B move ?
Must be the K because if it had been the P, as it has just been established that he passed through g3, the Kf2 would have been in check.

B) Let us continue our progress in the knowledge of the past.
We have established that the last B move was Kh1, but from which square did the K come?
If it came from g1, then it would have been in double check by the K and the R which, whatever their pasts, would have been respectively entitled to play Kxg1 and Rxg1 since these are moves of maximum length for each of these two pieces!
Well, cheer up, this point is soon écalirci. If the last move was Kg1-h1, the last W move (making double check) was necessarily Kg3-f2... which is not possible because the RB would have been in check by the bK.
Conclusion, the last B move is Kg2-h1.
To avoid periphrasis, we'll say from now on that the bK is "enlarged" to say that he is now condemned to play diagonal moves.
This kind of exercise is quite exciting because it develops the rigour of advanced reasoning in a medium more accessible than mathematics. This reason should be enough to put retrograde analysis in school activities, but I digress.

By the way, since we are talking about logical reasoning, the reader will have noticed that I have burnt a step.
I have indeed shown that Kg1-h1 was not the last move, but this does not completely allow us to conclude that the last move was Kg2-h1: for that, we need to be able to legally obtain the position with bK in g2 and wK in f2, Black to move. So far we have used Rule 1 to establish certainty. We now need to use Rule 2 to establish the various possibilities that are open to us.

C) What was the last W move , or more precisely what were the last possible white moves, to obtain the position (knowing that the last B move is Kg2-h1)?
A first (and simplest) solution is to say that wK was already enlarged. In which case, it was enough that he was on g3 (not in check and not in check either!) since both R's are enlarged. The W's then play Kg3-f2 (still not in check with their K and whether or not they are in check with their R is unknown) and the B's answer Kg2-h1. The position is reconstituted and legal. But this does not suit us, because an enlarged bK controls twice as many squares, and we have to checkmate.

Is there another way to legally obtain this position without having an enlarged wK?
Yes, by saying that the last W move is Ke2-f2 (thus checking Kg2). Note of course that this immediately implies that the wR is already enlarged to the maximum (moves of length 8 obligatory) because to be able to play Ke2-f2 it is not necessary for Rg8 to check Kg2.
Conclusion : We can therefore, as an option, have a totally free R but at the price of an enlarged K, or an K in full possession of its means but at the price of an enlarged one to the maximum.

We have completed the retrograde analysis phase. All that remains is to look for the solution to this direct mate in 6 moves.
Two paths of research:
Either wR is unconstrained and can go to checkmate a1 ... but then the wK is enlarged and the Ns can flee through Kg2!!
Either the wK controls g2 ... but the R is condemned to moves of length 8. It's not obvious, but that's where the solution lies!

To continue learning while breathing a little, here is now an imaginary dialogue between the Master and a passing visitor who has now assimilated the rules but is not yet accustomed to their implementation.
-The passer-by: Good grief, but it is of course! I even demolished the problem: there is mate in 2 moves by 1:Rg1+ hxg1= anything 2:Kxg1 mate".
- The Master : Well done. (yes, he always starts like that the Master, he encourages, but you always have to wait for the next part!). But a remark if you allow. If the Ws play Kxg1 they are enlarged and no longer control g2!
- The passerby : Indeed. Thank you, Master, but never mind. I still demolished taking into account your remark.
It will simply capture me one more hit. 1:Rf1!!! (to control g1 without enlarging the R!) 1:..b6 2:Rg1+ hxg1= anything 3:Kxg1 mate.
- The Master: Bravo! You are attentive and you know how to react. But one remark if you don't mind.
We are in a direct mate, not a helpmate. Thus, on your move 2:Rxg1 I suggest playing b6-b5! as I could not fear this ridiculous R just able to return from where it came since it is enlarged!"
- the passerby:...
There the report stops because he insulted Turnbull, which cannot be tolerated.
Of course, all this is not trivial and has a point in the solution that is.

When we are convinced (it is difficult!) that the R cannot mate, we say to ourselves that we must mate with the K. But Kf1-g1 does not mate because Kg1 is forbidden by Ph2.
We must therefore make its counterpart with Kxh2. The solution seems to be very simple with a mate in 4 moves: Kf2-f3-g3-h3!-h2 mate.
Where is the last finesse? The reader who has had the courage to last until now should take a minute to answer this question.

1:Kf3?! b5! 2:Kg3 ... draw! because the B's are stalemated ! (the reader is now expert enough to understand).
Holy Turnbull!!

Hence the solution which is now crystal clear. 1:Kf1!! (not to prove that the K is not enlarged, there is no need here to prove it since it is one of the legal possibilities as has been shown, but to prevent the defense by stalemate, which is a much finer and thematic justification of this key).
1:.. b6 (for, as the passerby had sensed, 1:..b5?? 2:Rg1! Certainly, Rg1 does not check, but it offers the Bs a move as forced as it is unfortunate 2:...hxg1 3:Kxg1 mate)
2:Kf2 b5 3:Kf3! b4 4:Kg3 b3 5:Kh3! b2 6:Kxh2 mate. Since Rg8 plays no role in the mate board.

#6 Growing Men

hs#3 Kobul Kings

hs=5 Kobul Kings

h#2 Take&Make