When i was writing about bitcoin i ALWAYS pushed back on the “complex math problem” analogy.

I used “lottery”. Miners can pull lots of tickets, etc etc

Pushing nonces thru a function ain’t “math” to me

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Lottery is a good analogy.

Although it's a bit more like constructing expensive, random keys that "unlock" the door containing the ability to write the next block.

For sure. Definitely an incomplete analogy (lottery), but useful when trying to explain it to the layperson