I think this skews toward programmers.

30+ questions and everything was a composition of shift, rotate, and, or, nand, nor, xor.

If you're a programmer it's just a matter of figuring out what operations are used. If you're not a programmer, you probably have no language to describe the relationships, and therefore can't just zip along looking for common assembly-language instructions.

EDIT: Now that I think about it, I bet I could make an increasingly challenging logic puzzle generator just by increasing the number of composite operations and operands. I bet if I googled I could find a dozen such projects that already exist. My work here is done. :)