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MatPlus.Net Forum Retro/Math Castling

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perhaps this ?

(= 2+13 )

a)
- If the rook moved last, 1. Rxh2[Ra1] 2. Rxa6[Rh1] 3. 00
- If the king moved last, 1. Ke2 2. Kxf3[Ke1] 3. 00
b)
We don't know which piece moved last, 1. Rg1 2. Rxg3[Ra1] 3. Kxf2[Ke1] 4. 000

it is even lighter

I would even prefer like this :

(= 2+13 )

ser-castling in how many moves? Anticirce

- If the rook moved last, 1. Rxh3[Ra1] 2. 00
- If the king moved last, 1. Ke2 2. Kxf3[Ke1] 3. 00
- If last move not known, 1. Rg1 2. Rxg3[Ra1] 3. Kxf2[Ke1] 4. 000

but... it does not work!

another attempt :

(= 2+13 )

ser-castling in how many moves? Anticirce

- If the rook moved last, 1. Rxc1[Ra1] 2.000
- If the king moved last, 1. Kd1 2. Kxc1[Ke1] 3.000
- If last move not known, 1. Ra4 2. Rxe4[Rh1] 3. Kxe2[Ke1] 4.00

Castling is illegal due to the black knight on e2 in the first two cases.

Anticirce: b8 is occupied, the black knight cannot capture on black squares

Of course it's legal and in 3rd case, 3. Kxe2[Ke1] only regains wK's castling right.

Ah, I see now; thanks. Anticirce and fairies in general can be muddling.

Brave stuff extrapolating sensibly beyond the normal coverage of PRA.

One minor cavil: I don't think that we should talk about "with PRA" vs "without PRA". What varies is whether we are optimistic or pessimistic about whether each piece has moved. In either case, under PRA (the default protocol these days) we then fragment the problem into twins, being as optimistic & pessimistic as guided, and while avoiding illegal combinations.

Here is a way to show the idea, close to what I am looking for.
(No need to recall PRA) :

(= 2+13 )

Anticirce
ser-castling : how many moves?

- 1.00 ? illegal due to retro analysis
- If only the king moved before, 1.Kxe2[Ke1] 2.00
- If only the rook moved before, 1.Rh2 2.Rxe2[Rh1] 3.00 (1.Rxh3[Rh1}+?; 1.Rf1? 2.Rxf3[Rh1] 3.00??)
- If rook and king moved before, 1.Kf2 2.Rxc1[Ra1] 3.Kxf3[Ke1] 4.000 (3.Kxe2[Ke1]? 4.000??)

Thanks Jacques. I particularly liked the exact arrangement of bPs on the Queenside.

An interesting way to avoid PRA by varying the move lengths of each case and by "rebirthing" either the K, the R, or both.
Reminds me of a direct mate twin where the move length gets longer as the number of white pieces on the board are progressively reduced.