On September 18, 2024, a 7225×7225 Sudoku (box dimension 85) with 25M blanks was solved in 10.7 days. That is 27 blanks per second on average. In fact, that isn’t how the solution works. Only a few blanks are solved in the first rounds of working the puzzle. Near the end thousands of blanks get resolved.
The computer is now crunching the solution on an 8100×8100 Sudoku (box dimension 90). That means that every row, column, and box or house contains numbers from 1 to 8100 only once. That means a human capable of discovering and resolving one blank per second (right) would take 1 year to solve the puzzle. That is assuming the person doesn’t sleep. In other words, any person claiming to solve this puzzle or anything like it step by step is in a fantasy land.
Because of the way the Sudoku is constructed, it is possible someone could figure out the pattern that creates these puzzles. That could certainly be done in less time. Good luck!
For me, I usually stop at anything larger than a 25×25 Sudoku called Sudoku 25×25 – how convenient! I use the Android phone app for those puzzles. It usually takes me 1-2 hours to do a 25×25 Sudoku. Finding the patterns in the solution is oddly relaxing.
So what is the purpose of creating and solving Sudokus no one is likely to do by hand? It forces us to re-examine how we solve and design algorithms for large solution spaces.