Comment by dataflow

So if I had to come up with a crossword solver, the first (dumb) approach I would try is the following:

- Come up with guesses for each clue (somehow—let's ignore the "how" for now)

- Prune all guesses whose letters mismatch with all the guesses for overlapping words

- Hopefully, you now have only one consistent solution set

Could someone explain why this approach doesn't work, and why you need probabilistic approaches?