How a solver tackles a numerical puzzle is up to them. Some will write computer programs, others will use spreadsheets whilst some will just use paper, pencil and a scientific calculator (PPC).
What sets the numerical puzzle apart is that you need to clear a window of a few hours during which you cannot be disturbed. Woe betide you get a phone call and your train of thought is broken!
With a cryptic crossword you can solve a few clues, put it down and go and do something else, then return and pick up where you left off. You can't really do that with a numerical unless you keep good notes!
The more you practice solving the numerical puzzles the better you become at spotting the way in and the strategies to adopt. In this case it would have taken me longer to type the clues into a spreadsheet than to do it with PPC.
Studying the clues very carefully before you start is the key rather than firing up the silicon!