World Draughts Forum

Are you interested by retrograde problems?
Let me first try to define what a retrograde problem is.
Stable position : a position is said stable if no pieces are in a capture position.
A retrograde problem generally start from an unstable position and the goal is to retrograde the position till a stable position but with a unique optimum suite of moves!
A suite of move is optimum (from the highest priority to the lowest) if
1) the number of plies used is minimum
2) the number of pieces added is minimum
3) the number of kings added is minimum

Just an example
The following position is a correct problem with a unique solution in 2 plies, 1 piece added and 0 king added


But this following one is not correct because there are two solutions in 2 plies, 1 piece added and 0 king added


Some problem can be extremely difficult but let me propose some "easy" ones, just to see if you are interested

Can you solve the five following ones (white to move):

_________________
Gérard

The rules don't specify it but I assume that white has the move in all these diagrams?

The examples:


And the diagrams:

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Hi Iljarn,

To answer your first question, yes in each diagram it is white to move (as usual for a problem).
Concerning the five diagrams you already succeed in 3 of them.
For the reader who is not familiar with such problem I will give the complete solution for these 3 diagrams:

Diag.3

White to play
Diag3 solution

Black to play
1...10-15 2.34-29 15x24
The solution needs 3 plies and when you compare the initial and the final diagram you can see that 2 pieces have been added and 0 king have been added. The score is then 3.2.0. I will write this with the six digit number 030200 which is the best (smallest) number you can get.


Diag 4

White to play
Diag 4 solution

Black to play
1...20-25 2.33-28 25x23
score 030200

Diag 5

White to play
Diag 5 solution

Black to play
1...21-26 2.28-23 26x28
score 030200

Let me comment your proposals for the first two diagrams
Diag 1

White to play
If I understand correctly you propose the sequence

Black to play
1...20-25 2.21-16 25x21
score 030400

You have to note here that you could get the same score from the diagram

Black to play

Does that mean that it is a dual and the problem is not correct? NO because 030400 is not the best (smallest) score!

Diag2

White to play

It is exactly the same situation in this diagram. You proposed a sequence with a score 030400, you can get easily a dual with the same score, but this score is not the best one.

Of course, for the time being, I let you and the reader search the solution for these two last diagrams

_________________
Gérard

030201 is smaller than 030400.

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Yes Ildjarn ... but it is not still the best score, and so the problem is always not solved.
I am fond of retrograde problem because you have to be very imaginative and skillful and, even with a very simple position (only three pieces here!), you can build quite interesting problems.

_________________
Gérard

For 16/11,21:

020601, 32-38 33x11
For 15/10,20:

020401, 4-31 36x20

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Almost perfect Ildjarn.
In the first diagram you can now very easily get the score 020501 which was what I had in mind.

_________________
Gérard

Oh, of course: 32-37 42x11.

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Congratulation Ildjarn!

Who will be interested if I post here some new retrograde problems?

_________________
Gérard

I like these kind of puzzles, but I doubt many people here would be interested, since you can't complain about the draw margin in these puzzles.

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Lasst die Maschinen verhungern, Ihr Narren...

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Schlagt sie tot -- die Maschinen!

Thank you very much for your answer Ildjarn.
At least with one person interested I can continue proposing such kind of puzzles.
I think it is a good idea to wait some days between each problem. So I will post a new position in 3 or 4 days.
Do you yourself built positions to be retrograde (but not necessarily a problem with a unique solution) ?

_________________
Gérard

As promised I come back here to give you some more retrograde problems

Let me remind you and clarify how to calculate the score?
First of all you count the number of plies : pliesNumber
Then you compare the problem position (i.e. the final position!) and the solution position (i.e. the initial position you have to discover) and you count:
piecesAddedNumber = number of pieces in the solution position - number of pieces in the problem position
kingsAddedNumber = number of kings in the solution position - number of kings in the problem position
The calcultatio is quite simple:
score = (10000 * pliesNumber) + (100 * piecesAddedNumber) + kingsAddedNumber

Note1 : pliesNumber is always at least equal to 1
Note2 : piecesAddedNumber is null or positive
Note3 : kingsAddedNumber can be null, positive or negative

The goal is always to get the minimum score.

In all problems it is white to play

Two problems for beginners:




and two others a little more difficult

_________________
Gérard

tries for diagram 1-3:

Still thinking about #4.

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Oops not so easy is it?
#1 :OK
#2 : your proposal is not correct because your start position is not stable. If you put black man on 23 (instead of 28) and you begin by 23-28 then the score is not the best.
#3 herer you can still get a better score!
#4 is more difficult

_________________
Gérard

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Lasst sie verrecken!

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