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cm - yes 7 cases are where you have the BCEF value as the answer, and the entry is G. The other 13 are the reverse ie you know G, and the entry is the BCEF value.

There may be a smarter way to proceed, but I determined the clues, where if you consider the answer as G, it was not possible to find a BCEF value. Therefore these must be in the first bucket, and so the entries can be readily determined and entered.

The way to determine if there could be a BCEF value is to establish an equation between G and B, C, E and F (involving only simple arithmetic functions and whole numbers). To do this, expand the equation at the start of the preamble.

Shout if you need further help.

crowdedmorning - Many of the answers that are in the G group (the group with 13 answers) would work as BCEF answers too. Just because you get a valid G when you apply the BCEF->G transform, that does not mean the answer should be treated that way.

Some of the answers can only work as BCEF, some work inly as G but most are ambiguous. You need to use grid logic to decide which is which.

Well, after quite a slog and a couple of bumps in the road using wrong values for some of the DURATIONS integers, I finally crossed the line this morning.
As AndyP, buzzb and others have noted, there are potential variations in the results from converting BCEFs to Gs and vice-versa, so it was essential to have all these written down to see which fitted together in the grid. And as noted, it also helped that there were no, or ineligible, alternatives in some instances.
I'm glad I persevered, although I think this should have been one for a long weekend!

v - TRINODUS - caused me no end of hassle until I noticed that there is an integer division, and any competent computeriste will tell you that integer division has to be approached carefully.

For the first time in a run of submissions going back more than four years, a Listener puzzle has defeated me. I have no maths background beyond O level many years ago. I don't use spreadsheets or coding in my work. As a writer and editor, words are my currency; however, I've struggled through every previous numerical during my solving career.

This one? I simply do not understand the preamble. I have no idea how or where to start.

I'm interested in others' views, especially those with my kind of background: does the language used in this preamble tip over into the realms of unacceptability ? Is there deliberate obfuscation (as often with word puzzles)?

I don't like letting my submission run end, but it would be gratifying if I learn that I'm not the only one totally confounded...

Hi orientfan,
Sorry to hear about your travails with this puzzle.
I do have a numerate (statistics) background but like you found the preamble well...daunting.
Key is getting the values of DURATIONS ( 1 to 9) in place. So that part is what I would call a 'conventional' numerical puzzle. These will give you 4-digit answers to the clue formulae.
For the grid entries, these answers are EITHER as BCEF values, ( so, e.g. 8923 would be 8=B, 9=C ,2=E 3=F) which you have to convert to a G value for entry OR they are G values that you have to convert back to a BCEF. You just need to do a bit of simple algebra to derive G in terms of B,C, E and F (and vice-versa), using the formula/expression given at the start of the preamble.
Hope this helps, it's worth persevering.

The key is to work out the equation for G in terms of B, C, E and F. And to realise all the answers to the clues are 4 digits, no zeros, no repeat digits.

Once you spot the first three or so of the 'Durations' numbers it all starts to fall into place quite quickly. As always square roots and powers are your friend.

I certainly think there have been much more difficult numericals in the last 4 years, so i think you should be able to get through if you do want to persevere.

As possibly the last post of this puzzle my question is: How does the value of H fit in to the picture when applying the equation?

It doesn't. It's completely irrelevant, other than to complete the initial preamble equation.

Yes, the way to obtain G from BCEF values could have been expressed more simply, with no mention of H and no radicals, but it's all working up to the gag in the endgame. I wrote bits of code to list BCEF/G values, and would have found it quite tedious to do by hand though I'm sure it's possible -- and I don't know how I'd have found the "five that exist" in the endgame by hand at all. The preamble looked really intimidating, and took a few read-throughs and a bit of thinking to realise it actually wasn't as bad as it first sounded. I think the puzzle was fair, though mechanically demanding, and very clever.