Time is mana
An inspiring lecture Street Fighting Mathematics by Ryan O’Donnell for general introductions to approaching theory-ish problems.
Indeed, most of time, we are jumping between an exploring scientist and a system engineer.
For some task, we develop a tool for others. Performance and stability are more important.
Some other task is to get a solution, whatever method you choose. In this case, all you need is to get to that goal! You could using brute force, or more sophisticated methods, but the most important thing is you need to get there!
Some interesting webpages to play with:
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http://oeis.org/ The On-Line Encyclopedia of Integer Sequences® (OEIS®)
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https://scirate.com/
