I remember my dad giving me the following problem on a long distance car ride:

An A4 sheet of paper, when folded in half, becomes an A3 sheet of paper with the exact same ratio of long side to short side. Given this information, can you figure out the what the ratio is?

I must of spent 3 hours of that car ride doodling on a piece of paper trying to nut out that problem with no additional information or tools, ultimately unsuccessfully.

To this day, I think that was when the light switch went off for me about math as a creative problem solving endeavor and not just a rote series of calculations.