This is one reason I created Chrome-8, cited from the now un-funded MegaMath project (created by, among others, Nancy Casey):MegaMath project at Los Alamos National Laboratory

The source of new problems, discoveries, and theories in mathematics is mathematicians’ own inventiveness and their propensity for asking “what if” kind of questions. Students who puzzle over existing questions or ask new questions of their own are doing mathematics. When students play games on graphs it is natural for them to ask two types of questions that get to the core of what professional mathematicians who are graph theorists do. These questions are:
How will this game change if we play it on a different graph?
What if we changed the rules or invented a different, but similar game?

Give it a try!

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