How do you solve this... without writing a brute force solver

I remember writing an recursive algorythm for it in my college days. Which is basically brute force croocks algorythm. You could do stochastic, randomly place numbers until number of errors is 0.
The example is very croocks, only place numbers where there is only 1 possible, recalculate options for errors, implement or try other, place next.

There's tons of cool sudoku algorithms...