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One of the most satisfying things about cryptic crosswords is that the clues are self-checking. The wordplay checks the definition, and vice versa. A recent numeric puzzle also achieved a degree of self-checking, by combining puzzle and sudoku.

Not the case with this puzzle, unless I've missed something (which is quite possible given the number of distractions today...). But if I've made an error I might not find out about it until quite a way down the line...so, with the NE half pretty well complete, can anyone please confirm that 7 is 241, and that the same 3 digits appear in sequence in row 3 ?

Hi Meursault

Yes you are correct.

Yes, I agree with those, but I reached an impasse with about half the grid filled when I could not reconcile my options for 13 and 31 with the required equality of digit sums, so I've put it aside to rewind later.

DJA, thanks, much appreciated.
Throck, I'm not quite as far on as that, I'd also put the puzzle aside...but I'll give it another hour or so now.

I'm a complete novice when it comes to The Listener, having only tried the last 4 or 5, and never a numerical one, so please be gentle with me! I do the Guardian Cryptic every day and also broke the Enigma Code during WW2. Actually, that's not true.............. I don't do the Guardian.

The only one I've written in with any certainty is 1.
I have 2 options for 2; about 15 options for 3; 5 options for 4; I can see relationships between 4, 11, 19, and 16. I have deduced a couple of other 'facts' on 22 and 32 from the 'statements' provided.
I have lists and lists of 3, 4 and 5 digit cubes, prime numbers, etc
I have a few "if that is....... then that must be....... but then it means that that can't be......"

What I'm missing is the breakthrough that enables me to start writing some more in with certainty. I don't want anyone to tell me answers but if, from what I've written, you could give me a nudge in the right direction, I'd be very grateful...... thanks!

And yes, I do the Guardian every day.

Throck, firstly you should be able to get further without needing to worry too much about 13 & 31. Though I don't have entries for either of those two yet (and probably won't this evening, since I'm falling asleep), I now have all the NE half and a good deal of the SW half filled.

I think the puzzle mostly requires solving in a certain sequence.

For 13, the last digit must be 1 since 21 must begin with 1. This gives just 4 eligible prime numbers between the values for 7 and 19, with a maximum digit sum of 11. In turn this eliminates many of the possibilities for 31, for which at the moment I have ??31.

Many years (decades) ago, I used to be a computer programmer. I'm sure I could still write a program to solve this puzzle.

Simond9x, welcome.

From entering 1, you have 2 possibilities for 2. 14 is a multiple; has to have 2nd digit 1,3,7,9; can't end in 0, reversed is >613 and prime: this leaves just one option for 14, which may be entered, thereby also solving 2. I really can't remember precisely my sequence of solving after that, but much of it was in the NE corner, involving tabulating the various possibilities for the square and cube entries. 22 can be worked out quite easily, at least to 2 possibilities. 4 has very few options, I solved 8,9,12 and 16 in the same phase of work.

Use online help for prime number lists, square and cube lists wherever you can. For working out the possibilities of multiples, I found a simple formula on spreadsheet very useful. At the end of the day, it's just number crunching, quite tedious and without any of the rewards of being able to say that definitely the outer fringes of the universe will remain behind as the rest of it collapses...

Ha ha! thanks for that. I'll give it another go in the morning and report back.

Meursault,

Thanks. Looking very quickly at your first hint.....
"14 is a multiple
has to have 2nd digit 1,3,7,9 ........ understand
can't end in 0 ........... understand
reversed is >613 and prime" ......... understand

....... just not sure where the "14 is a multiple" comes from?

Sorry if this is painful for you.