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A real Radix mathematical stinker. I can see that EFEETELY + HINDUISE = MOTIONED, but where do the 2 letters O and F come into it? And how on earth do FRUITION and GREEN BAN lead to --A-T-ON (with the 2 letters T and H)? Clearly a long way to go.

cockie,

I'm in a similar position (of confusion!). I've got all the normal clues, but not many of the pairs. The difficulty, of course, is in making any sense of this bit of the preamble: "calculations systematically related to the clues' treatments".

Cockie,

Looks like sometimes you have to multiply the letters instead of adding. Wouldn't be surprised if there's some divisions and/or subtractions in there as well.

Cockie - you have to add or subtract letters from the CLUE so for example fun dies becomes undies.

Thanks unclued, but I'm well past that stage. The idea of multiplication hadn't occurred to me - merely addition and subtraction. I expect raising to the hexadecimal power will be needed at some stage.

Cockie - have you got the source yet? Any help appreciated.

Unclued - I got it from looking at the last half dozen or so of the 18 normal clues' extra letters. It is of the form X by Y.

Cockie, you need to think about the three ways that the double clues can be treated. They should suggest three ways of carrying out calculations. Now experiment with what you have at 1ac. You should end up with a word meaning, among other things, 'the front of a dress shirt'.

But I'm struggling. I've solved 7 of the double clues completely but I only have one half of 6 others, i.e. out of 36 clues I've solved only 20. I can't see me finishing this one.

I still don't understand the logic for which process to apply to the double clues, Ionacarr. I have only solved three of these, all of which required a letter to be removed from one of the two clues and a letter to be added to the other. But one of the three required one process and the other another.
Like others who have posted here I am really struggling with this. I've solved 12 of the normal clues, but letters in the grid give zero help in solving the double clues which seem to need to be all solved cold. I hate such puzzles and only my liking for Roddy, with whom I always had a pleasant chat at the annual dinners, persuades me to continue. Does anybody who has solved everything care to give a few hints? The ones I've solved are 1ac and 14 & 15 dn.

The other doubles I've solved completely are 19, 21, 25 and 26dn - happy to help with the treated words in these, as follows: 19dn = CE and fluter (but the parsing of the latter mystifies me); 21dn = hairline and trebling; 25dn = commander and weigh; 26dn = sold and charmed.

What infuriates me about this puzzle is that I have the title, the quote and its alteration, part of the source and the systematic method (which incidentally appears to be randomly assigned to the clues, unless I've really fouled up - I took 'systematically' to mean 'related to the methods used by this branch of maths' as opposed to 'specifically' to each clue).

But, the infuriation: I *know* from the quote what all the letters are that give rise to the treatments, but *I still can't make sense of 16 of them*. Slogging away when all the PDMs have happened seems to me to be counter to the enjoyment of a puzzle. I know the Great Man is revered, but I feel he's broken a precept set by Ximenes, that the solver must always have a fair chance of defeating the setter.