You should be able to do it in under 20 lines using the same matrix operations as the K code via numpy.

Numpy is indeed very apl. Just more horrible to me; not python-y and annoyingly verbose for the apl-er.

A few years back I made a modest attempt at writing a concise yet readable sudoku solver in Python - in about 29 lines: https://github.com/hrzn/sudoku/blob/master/sudoku.py

Could have been made shorter at the price of readability.

Looks nice. Since imports numpy can utilize (more of) numpy's operations to squeeze validation functions and nested fors to one. Should result in shorter code but readability will probably depend on reader's experience in array programming.

It probably isn't. At least, not for Python.