[Retros] Retractor v2.2 with cage verfication released

Theodore Hwa hwatheod at cs.stanford.edu
Sat May 20 18:03:35 EDT 2023

Hi all,

In a previous message [1] I discussed a cage verification algorithm for 
improving the solving capabilities of Retractor. This has now been 
implemented in Retractor v2.2. As usual, this latest version is available 


You may need to do a hard refresh (Shift-refresh) if your browser has the 
previous version cached. Make sure it says "Welcome to Retractor 2.2".

To learn more about the cage feature, with some examples, click the 
"Cages" link towards the bottom of the Retractor page above.

Cage verification is a form of human-assisted solving, but still fully 
verified by the computer. When humans supply appropriate cages, Retractor 
v2.2 is able to verify them and then solve an additional 23 type A, 24 
type B, 7 type C, and 16 type D last move problems at [2], compared with 

As a quick example, consider the first problem 8/011 at [2], 
8/8/8/8/8/1P6/1PkPP3/KR1b4 (last move?). Initially, Retractor is unable to 
rule out the incorrect uncapture a2xb3. However, after the incorrect 
uncapture a2xb3, the lower left corner (a1-e2 rectangle) forms a cage 
because that configuration can never be unlocked no matter what we do 
from here. In Retractor v2.2, the user can input the position in the a1-e2 
rectangle as a cage, and Retractor can verify the cage. After that, 
Retractor can rule out the illegal a2xb3 and find the unique solution to 
the original problem.

Any comments or questions are welcome!

Ted Hwa

[1] https://pairlist1.pair.net/pipermail/retros/2023-January/004983.html
[2] https://www.janko.at/Retros/Records/LastMove/index.htm

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