Deblurring algorithm to precede thresholding - speed over accuracy
You only need to find and report positions of nine specific symbols.  You can do this by computing correlations (done quickly by multiplying in Fourier space) with samples of the nine digits snipped from a typical puzzle image, blurred as it is.  All blurred '9' will look the same, and likewise all other digits.  I'm assuming puzzle images are taken with the same camera the same way.  

It might work better working on high-pass filtered versions of the input puzzle image and image snips, by subtracting from each a more-blurred copy.