Even if his symbolism led to the logic gates of the modern computer, I still need someone to explain the precise advantages of the Boolean approach to this kind of puzzle over the succinct classical type of reasoning presented in the first paragraph in the above solution.
For one thing the original article on this website appears to promise us something better, and presumably quicker, than "trial and improvement". Yet both methods presented entail two steps: trying the first then the second statements to see what would follow from supposing them to be true, and finding them to result in contradictions. All that Boole seems to provide here is an extra layer of symbolism to decipher. How does it help specially, for example, to know that Xr + Yr + Zr = 1? And that it is contradicted by Xr + Yr + Zr = 0?
I could be missing the point of course, perhaps in hoping for some kind of algorithm or set of arithmetical rules that can be applied unthinkingly rather like steps in long division.