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Trial and error is a perfectly acceptable mathematical process. For me this was a delightful puzzle using multiple copies of the grid, a pencil and scientific calculator. It all falls out very nicely. No need for a spreadsheet or heaven forbid AI. Thanks IOA for an enjoyable couple of hours.

I thought it was great. Got close to the end and realised the diagonals didn't work. Found my error and it fell out fine second time. No trial and error, just eliminating Impossibles. And all doable without even using a calculator. Great stuff.

Loved this puzzle! It was definitely challenging but, other than printing out a list of Primes, did it all with pen, paper & calculator.

The diagonals are crucial to keeping this an exercise in numeric logic, and not brute force calculation...

I always appreciate a tough but fair Numerical which can be solved without recourse to a spreadsheet (and no pesky anagram at the end this time). Progress was straightforward except for a small blip when I overlooked that there are powers greater than cubes (duh).

Thanks IOA!

Finally finished this but I'm not as enamoured as others as I too had to resort to brute force - i.e. guessing. I would love to know how this can be solved by logic alone as my logic failed with only 2/3rd of the grid filled. The RH column was my nemesis as I couldn't see how to eliminate the copious possibilities I had for 3d and 4d. The sudoku itself was difficult, never mind the scarcity of the clues. I've double checked the clue solutions and the final grid, and nothing seems incorrect, so I have been lucky. Not my favourite numerical due to my logic failing me rather than the puzzle itself.

Three times I've started this and three times (8 hours+) I.ve found an impossible barrier (2 answers the same). I would welcome a small hint, being the sum of the 5 digits at 10D/16A. I have 5 possibilities, two the same. If any kind person wishes to help privately I'm at arthurswan AT btinternet DOT com

I thought the genius of this puzzle was that you needed all the clues in order to solve it without trial and error. I thought by the time you had enough digits in the grid to be worrying about 14ac and 13dn it would be just sudoku logic but, no, all the clues were needed!

SUDOKU-wise this was a very clever puzzle because it gave rise to lots of 2-way options, esp in 3x3's but also in rows & columns: too many to chip away at with Brute Force (unless you are a lot more patient than me!).

Analysis of 14a actually left only one possible set of solutions from those available for 3d & 4d (less than you might think, given other known info...; 13d had more options but submitted to similar analysis.

These answers then allowed methodical resolution of those binary options.

There was only 1 solution for three of the clues, then another three clues with 5 solutions each, then one clue with 10 solutions, and finally two more clues with over 20 solutions. This makes it impossible to solve in spite of Sudoku restrictions, without recourse to mind-numbing trial and error. One more clue like 10across would have probably made it solvable by logic alone.

Byron

Hi. It was solvable by logic alone. You could rule out most of those options by how they interacted with other clues. There was no point where I entered a number in the grid without being sure it was right (apart from when I went wrong the first time through😄).