Isee, I've been working through this and get the attached image, working backwards.
Some interesting geometries there, with the 8 squares around the centered unit square.
Just a way to picture our original layout, with a specific solution for c=259.
Also, note other image attached (taken from the Wolfram page Isee *linked), remember the CONWAY hint?! I'd been looking into that particular Conway and Guy book too, ding ding.
BTW, regarding hints that came with that CONWAY one, VQC mentioned "asymmetric warfare". Have been thinking maybe this is asymmetric, as in "Asymmetric Encryption" algorithms = "Public Key Encryption"?!