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This was more fun than I expected, with constant successful nibbling, until my current impasse. I have 18 of the letters, a full third layer, but stuck on "a".

I've made sensible words for the 1,3,4 and 5th words, but the second one seems to be giving me something which relates to the title, but which I have no idea of how it could be applied to the digits.

It's a ten letter word and you substitute the first letter for each zero in the grids through to the tenth letter for each 9 in the grid.

The four grids are then entirely full of letters and it all becomes clear

Thanks Tatters.

I realised I'd got confused between "a" and "A", so i filled the grid. However, I don't think I'd ever have got the interpretation of the second word. Very clever, and how it was constructed, from words to digits to clues, amazes me!

I only had to restart once for a change, as I kept confusing the correct numerical value with that which creates the cube. The only niggle I have with this is that I found it virtually impossible to distinguish a lower case "L" with an upper case "I" in the clues. I found most of the numerical solutions in a linear and unambiguous manner, but the last few did cause me a headache. Overall, a most enjoyable and clever puzzle.

If you know something about computer programming and want to try something other than excel for help in solving these sorts of puzzles then I recommend looking at python. It's got a feature called List Comprehensions which allow you to do things like: Tell me x and y where x and y are both in a certain set of integers, and x * y is a 6 digit number with the second to fourth digits being 123.

They were all upper case I with the exception of 15a, as indicated in the second paragraph of the pre ramble. This was certainly some feat to arrange 48 words using just 10 letters into a 4x4x4 cube as the basis for a numerical puzzle - bravo Elap!

crosswhit99, the preamble could have been an indicator that there is a lower case L and not an upper case I. I tend to find that making assumptions with numerical puzzles always leads to a whole world of pain - so I left those clues to the very end!

In that case the editor would probably have insisted that the rubric stated there was no upper case I in any clue rather than simply referring to one clue, though admittedly editors can't always be relied on when it comes to making pre rambles completely unambiguous ;-)

Absolute belter, well done Elap. The numerical bit was challenging without being ridiculous and you could make steady progress. The denouement is absolutely stunning. God knows how long it took to come up with that. Brilliant.

I was going along nicely until I came to 14a, which I cannot fathom. I assumed I had gone wrong, so started again but still came to the same answers. Could someone please tell me what i and I are. I originally had i as 96, which would fit with the first word.