I've managed to optimize it after profiling for few hours, but it still takes almost 10 seconds for those 100 tests. Insanely hard.

Your diagnostics seem to be terribly wrong, because it seems to me that you are printing times of each recursive sub-call and not of a solution as a whole. After measuring total times of your solution, I got following logs:

Solved 1th sudoku in 0.67274213
Solved 2th sudoku in 0.13053465
Solved 3th sudoku in 0.50209308
Solved 4th sudoku in 0.49838281
Solved 5th sudoku in 0.09900117
Solved 6th sudoku in 0.04873729
Solved 7th sudoku in 0.04066420
Solved 8th sudoku in 0.22643065
Solved 9th sudoku in 0.03949404
Solved 10th sudoku in 0.04394507
Solved 11th sudoku in 0.20175838
Solved 12th sudoku in 0.28576541
Solved 13th sudoku in 0.10822368
Solved 14th sudoku in 0.03941178
Solved 16th sudoku in 0.08698726
Solved 17th sudoku in 0.15653372
Solved 18th sudoku in 0.04665780
Solved 19th sudoku in 0.12197948
Solved 20th sudoku in 0.16618562
Solved 21th sudoku in 0.16748643
Solved 22th sudoku in 0.10031271
Solved 25th sudoku in 0.08102345
Solved 26th sudoku in 0.16066670
Solved 27th sudoku in 0.09649348
Solved 28th sudoku in 0.10229945
Solved 29th sudoku in 0.16057420
Solved 30th sudoku in 0.38737392
Solved 31th sudoku in 0.15400934
Solved 33th sudoku in 0.05073357
Solved 34th sudoku in 0.10549068
Solved 35th sudoku in 0.50075221
Solved 36th sudoku in 0.15533233
Solved 37th sudoku in 0.10187721
Solved 38th sudoku in 0.04199123
Solved 39th sudoku in 1.79772639
Solved 40th sudoku in 0.34626746
Solved 41th sudoku in 0.04284692
Solved 42th sudoku in 0.10607004
Solved 43th sudoku in 0.51317811
Solved 44th sudoku in 0.14717102
Solved 45th sudoku in 0.06041265
Solved 46th sudoku in 0.22008801
Solved 47th sudoku in 0.14626503
Solved 48th sudoku in 0.14514446
Solved 49th sudoku in 1.39359808
Solved 50th sudoku in 0.22236490
Solved 51th sudoku in 0.34508967

It seems that your solution handles some cases poorly, because times go up to 1.5s+

I can send you my implementation of the solve and measurements later if you want.

Python

In what language?

A year is a little extreme, but glad to see you did it!

It was very difficult for me. I even gave up CodeWars for a year because I couldn't solve this problem in 2023. I don't like my solution because it's clumsy. But it worked! I'm glad I was able to solve this!

good for you man, im still timing out from using the backtracking approach :(

EDIT: I'm sorry, i used some code on github for the solution. Before anyone says anything, I probably shouldn't have done that, however I have spent some time reading the code, and I can fully understand it now. I think the point of codewars is to learn, but sometimes give up if it is too difficult. And for the reason why I did that, well, it's late now, so I got frustrated and just copy pasted some code off the internet.

This was a very challenging and fun kata! It required a lot of thought about which data structure and which algorithm to use to minimize the number of computations. In the end it was worth it and I managed to pass it marginally.

well, this one is insane

A correctly composed Sudoku must have a unique solution !

timing out from backtrack :(

js plz

Its 5 per test.