Really interesting idea, I like it. Obviously difficult in practice, but the spirit of the idea makes sense, as long as the numbers get large enough.
Discussion
Ok, I give up, ðŸ˜ðŸ˜ðŸ˜.
What's the answer ?
No, you succeeded I'd say, that last idea feels like a valid solution ... unless i missed something. I'll post the 'intended' answer later.