TLDR Shannon's approach to creativity and few mental tools for problem-solving:
* simplify by eliminating everything from the problem except the essentials; cut the problem down to size
* seek similar known problems, find analogies and apply solutions to your problem
* try to restate the problem in just as many different ways as you can
* generalize the building blocks by trying to apply them to broader class of problems
* structurally analyse the problem - break it down into sequence of smaller mental leaps
* invert the problem and see if it's solvable by retracing from solution to the start