IF you admite the picture is symmetrical, there is "only" 12 solutions. Indeed, there are 6 solutions in the area R3-5C9-12 (and its symmetric), and there are 2 solutions in the area R15-16C11-12 (and its symmetrical) which are independent. In addition, symmetry is unfortunately not a proof of logic. It's a shame because the picture is beautiful.
It's a shame because the picture is beautiful.