I get that mathematicians make up problems to be "interesting" and chewy to solve... but I keep coming back to one thing when I read through the article... WHY? The initial ruleset is just a human construction. It's a pattern that humans created. Why should it 'mean' anything mathematically? I know the value here is in the process, and there may be interesting other mathematical principles that are developed or evolved from the process of answering these three questions. But why this problem? Is it just mathematical curiosity that hooks certain brains, and makes problems like this interesting to a specific thinker? Or is there more here that I am missing...? (I'm thinking about a painter looking at another's painting... the brush strokes, the colors used, how those colors were mixed, the substrate that is being painted on, etc... is that analogous?)