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#12 and #18 This puzzle doesn't need an end game given it's tough nature. If there had been one then many solvers would have been deprived of tackling it.

The end game in a numerical has only really come in since the puzzle moved to The Times some 30 years ago. It is supposed to make it more appealing to crossword solvers but can make it less appealing to those who like their mathematicals straight with no chaser or after!

A lot of the mathematicals that appeared in The Listener magazine were ferocious beasts and you had no internet or computer to help. You should try and solve some of them using what was available fifty years ago in order to fully appreciate that nowadays we have it easy!

This arrangement is called a right hand dice - who knew? - and maybe I went about it in a different way, but I found it very helpful in eliminating some possibilities early on.

Oyler - I wouldn't say any puzzle "needs" an endgame. Only that it is my personal preference that they have one. I cut my teeth on years and years of soulless sudoku books. I grew bored of the idea of solving simply to fill in a grid. An endgame gives me a goal of something to work towards. This is true for crosswords and numericals in my case.

While nothing in my comment was intended to discount the usefulness of computer aids, I did grow very curious to try a numerical from 50+ years ago. Unfortunately I can't seem to see back that far from my subscription to The Times.

Cypher.. Can't do you one from 50 years ago but there are several in the Listener book dating back to 1997-2000.

https://www.dropbox.com/scl/fi/711wauzivoejjbzfpfsdp/3490.pdf?rlkey=hurqi3d009mywkkksor8uzemq&dl=0

is an example for you to play with and I have the solution if/when you need it.

Thanks Jordan! I'll give it a go!

I don't know, because I haven't quite finished and have more compelling things to do this evening, so I may come a cropper in the last stages. However, my impression is that, to avoid too many options that need to be laboriously eliminated, one needs to approach the questions in the correct order. Which order might be an appropriate nudge somewhere along the line.

cypherhouse. There's also a first book of The Times Listener Crosswords 1991 - 1995 as well. If you wish to try some that appeared in The Listener magazine then email me at oyler@crossnumbersquarterly.com and I can send you a few!

Got over the line after 2 false starts. I didn't find it intellectually challenging or fun but just a bit of a slog narrowing down possibilities. One of those puzzles that is impressive in terms of the setting rather than satisfying for the solver.

That's my reaction to most of the numericals. I'm always impressed by the skill in setting them, but there are very few cases in which I can see the solution being deduced in a purely logical sequence without testing several possibilities. Happy to be corrected, but if I'm right then to me that's not fun.

I'm struggling here… I started off wondering where the way in was. Then I read the preamble again and got the impression that the die illustrated was the first throw that IOA made. Despite wondering why the 1, 2 and 3 weren't printed in the top left cell of each grid, I forged ahead with these entries and made some progress.
But today, I reread the preamble and now think l probably need to start again…
Normally we are told that each entry is unique, but I see that is difficult here as an entry may be the answer to a clue OR the top, front and right-hand face of a throw of the dice.
Queries:
* As there are 24 distinct throws possible but only 16 throws made, is it safe to assume that each throw is unique?
* Can we assume that 1 is NOT one of the values of W, X, Y and Z, as they are each used in at least one clue in a non-trivial (is that the correct mathematical term?) way?
* "Some number…" in T1dn and F4dn seems to be so open-ended as to indicate a myriad of possibilities, but the power of… er… "power" means that even 2^n quickly becomes a large number. Is this the way in?
Any help would be gratefully received.