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Finished finally. Impressive to find enough numbers satisfying all the requirements to make this whole thing work. Gitto - I can confirm my earlier post was correct.

To me that was a perfect puzzle. I particularly liked that the difficultly remained high throughout the solve. Sometimes I find that once the initial barriers have been passed the rest of the puzzle can seem too easy/repetitive, but this one had me pondering over every step. The ending was also very satisfying once I had spent time pondering that too - I was glad for the 9,5,6 hint as otherwise I don't think I would have got close to figuring out what to do!

So thanks Elap for an enjoyable Saturday evening's entertainment.

I have a completed grid and the 9,5,6 instruction.
But that's as far as if goes.
My question is, do I *need* to understand the relationship to be in a position to submit?

I don’t see how you can have the two unclued entries unless you understand the relationship. For me, cracking the (9.5.6) was the hard bit. The instruction is unambiguous, and the relationship between the two pairs in each set was one of the first things I checked.

I think that I have worked out what to do. In each of my sets (including sets 7 & 8), I have two answers with something in common. In all bar sets 1, 2 & 6, the other pairs also have something specific (but different) in common. Including those three sets, what those pairs each have in common is more general.

I can't see that my grid can be wrong, given how the numbers and message work, but I'd appreciate confirmation of my description.

I hope that the above gives nothing away to those who haven't solved this puzzle!

I can see one unclued answer that must require solution of the clue and the resulting process. What that process is is still unclear to me, but this puzzle is so good that I'm happy to just stare in wonder and wait for the penny to drop.

I, too, assume that there's only one coherent or consistent fill that produces a clear clue.

Rhsl - I'm afraid that doesn't sound right. I don't see how you can have the right answers for the unclueds without solving the phrase. Once you have the phrase you see exactly the same relationship for every set.

Thanks, SH.

I have an X and Not X relationship.

I would have expected an X and Y, but three answers don't fit. The two unclueds are X, so I'm happy with them. I can't see how to make it X and Y, though.

Thanks Candlestick. I had overlooked that there are three options for 7dn.
However, am I correct that there is only one option for 19dn?

I think my difficulty is not knowing exactly what to apply the instruction to!

If you've worked out what's going on you'll be in no doubt at all about the unclued entries and the pairings.