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You could have two points in 2 of your non overlapping bands that are less than a band's width apart.

Also, the probability of the first 2 points will always be 100% because they define the line.

Also, it's not 7 random points, it's 7 of thousands of random points.

Alright, I suppose it's not as simple to formulate the question accurately and correctly.

> Also, it's not 7 random points, it's 7 of thousands of random points.

Ah - I missed this one.

But diagonal at what angle? :)

I think if you set the probability of the first one at 1, then the rest works perfectly at any angle of band. I could be wrong, but intuitively that seems correct.

search box tells me 600 choose 7 is 5e15, which implies (if google and GPT4 were correct) that there ought to be on the order of thousands of fat lines containing 7 actual cathedrals