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I always look forward to the numerical puzzle which is sadly only once every three months. This one is really delightful, I urge anyone who is baffled to stick with it. Unusually, although I used a spreadsheet to help keep track of my progress (with each clue listed as a formula, a trick I always use) I didn't need a single macro - there is a path through without resorting to writing any code - all of the arithmetic can be done without a computer or even a calculator if you fancy a real challenge!

Apart from the hint on factorials at the very beginning of this thread there has been no request for a hint so here goes. I have no access to spreadsheets or programs so am solving by trial and error, which was OK for the first half but there are some letters only appearing in clumps and there being two of each to consider is making the trial some what extended. A gentle hint as to the ordering by size of these letters would cut down the slog. CALME Thanks.

Using the expert as the key the Playfair encoded ascending sequence is

IBLACRBKESSQUPQO

If that's a reply to my query, thank you but playfairs are beyond me. All I need is for some kind soul to place A,C,E, L and M in order of size. Thanks again.

How about this: the order you have written is almost correct.

Crowdedmorning, the paraphrase is five words, and includes a past participle and a contraction.

Murky,

I got it fairly soon after that post but thank you! As it turns out, after solving this entire puzzle, I made a simple arithmetic error in the most straightfoward bit, the alphabet cypher. I did the sum incorrectly at least three times before realising my error. Go figure.

Thank you mathprofrockstar your hint was sufficient to do the trick.
I had been bogged down by 24d when couldn't understand why O was not a factor of C.

Panicea, you were not alone regarding 24d. It threw me for some time.

Could someone please post the text of the rules? I'd be most grateful.

In my attempt to tear out the puzzle from the paper to save for a rainy day, I've managed to keep the grid and clues but not the rules!

I can roughly remember that each letter has one value in across clues and either one higher or one lower in the down clues. Can't remember anything about the coloured regions or what goes in the boxes. I always try the numerical listener. Be a shame to miss this one!

Thanks in advance.