Dear StrmCkr,

I want to thank you for continuing to look/answer my DSS questions. I'll try to answer your questions and give you the lastest info on my RN/CN/BN efforts:

This might sound stupid, but can the DSS rules be applied to RN/CN/BN transposed spaces?

as individuals? should work to find hidden naked triples pairs singles. in each plane as its own interface.rn. cn. or bn.

then combinations of those to find larger ones? is that what your suggesting?

My question is whether or not I can apply the standard hidden subset rule for eliminating candidates outside of the subset in each cell participating in the hidden subset. This is effectively the same as finding a naked subset of size (9 - sizeof (hidden)). I'm in the process of coding/debugging this. So far, I can quickly find ALL DSS size 2-4 very rapidly in RC space (less than 1ms) and that includes all normal naked subsets size 2-4. Perhaps that answers your question about the subset <256> for r123c3. It's actually the very first DSS that I have in my log

- Code: Select all
`do_dss - disjoint subset <256> at r1c3 r2c3 r3c3`

but there were no candidate eliminations detected. My test program only performs DSS analysis, so any missing naked/hidden singles or box/row/col coloring or other reductions are missing on purpose. I start with a grid from a known position (usually using Simple Sudoku SSTS) and then test to see how many reductions are possible and what size DSS subsets are most productive etc. I've added it to my full-blown solver, but placement in priority of algorithms is critical. Currently, I'm using it as a complete replacement for my normal subset processing, and while DSS is slow compared to standard SS, it finds many more reductions. My belief is that if I can get the hidden DSS to work correctly, I won't be plagued by the slow processing of scanning for DSSs > size 6. So regarding the combining of subsets to find larger ones... I've tried that, but it really isn't any faster than what I'm doing now. Problem with combinations is that you still have to check all smaller sized subsets for completions, so at size 7, you're still looking at all the size 6,5,4,3,2 sets. Combining was actually slower than my current recursion for some perverse reason -- maybe I didn't code it as efficiently, but the number of combine tests was still in the billions for size > 6.

As for subset counting... I've pretty much abandoned that for later study since it's so painfully slow.