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I'm confused by the nomenclature used in this. For instance, the last across entry has small type for HEN suggesting that it is T^(H+E-N), but there are no brackets in the clue. So is the 10th across clue (HI)! or H(I!)?

Gitto,

I’ve made no meaningful deductions and am quite stuck but I do think I’ve determined HI! must be H(I!), otherwise the puzzle numbering breaks elsewhere.

chrisremo, I had come to the same conclusion, but starting a mathematical with an assumption is fraught with danger, but here goes............

I've interpreted HI! as H(I!) and have a completed grid, so feel confident in saying that's correct. A quick online search suggests factorial takes precedence over multiplication by convention.

For those who have been put off, take heart: it looks horrid at first, with its carte blanche and non-integer answers, but I'd say it's no harder than any other puzzle of the map-letters-to-numbers type. Maybe even easier than some other examples of the genre. That sounds like bragging on the part of this solver, but I think it's a fair assessment - the puzzle just has an intimidating exterior. (I won't say *why* I think it's approachable as that would give too much away.)

Agree with smsl. I nearly didn't bother when I read the preamble last night, but I solved it steadily it this morning with just a calculator and some simple logic. All I would add by way of advice is to focus on the clue numbers first.

Incidentally, if HI! meant (HI)!, not only would that be contrary to normal conventions but you would rapidly run out of candidates for an answer limited to eight digits.

I found this a bit underwhelming. You can work out almost all the letter values just from the clue numbers as the grid must contain all the clue numbers between 1 and n. Then a tedious slog calculating answers to fill the grid. I gave up half way through when it was clear my letter values were correct.

I cannot get started on this one. The only thing I have so far is that the number of the seventh down clue must be even, which severely limits the possibilities for U and S. Is this a place where others have started?

Not sure why that clue number must be even?
I started with (SH)^Y if that helps at all.

Spectator, I decided that US could not be 5, 7, 9, 11, or 13 and so therefore must be even.

Remember U or S could be 1.