I've also used that explanation before, but I've found a new one that's more technically accurate and easier to understand. Computers compete with each other to find a unique identifier, which must have a variable number of leading zeros.
Although correct, I think it's still too abstract, and more contextual information will be needed for a non-tech person to truly understand. For example, what purpose does it serve? Why is it important? etc.
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The WHY is a different question but you are correct. I think the why is easier to explain actually. We often skip the why and I think that's why people have a hard time with bitcoin itself.
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