Tower of Hanoi
[Sec Maths and above: Number Patterns / Functions]
You've heard of the Tower of Hanoi puzzle, probably. That funny rings-and-discs thing you see around kindergartens, or some leisure rooms etc. You have, probably, either played it yourself or at least seen an instance of it being played. (If not, this video would be quite a treat.)
I think it's fairly self-explanatory, but yes, you can derive it by charting the possible outcomes of each state.
In primary school, your questions tend to be much simpler, if you recall. A man jogs around a track at a constant speed, the variables do not change, and you simply apply the [distance = speed x time] formula to derive the answer. However, you would quickly realise that it is indeed a very simplified pattern, specifically tailored for children to get comfortable with the concept of patterns.
Yet, we can observe that some of the more complex patterns behind the Tower of Hanoi were built under simple patterns compounding into a big complex. Mathematics, at times, tend to function much like a machine; and there is a certain sense of wonder when you do decipher it yourself.