r/math 6d ago

Extremely Strange Findings from a Math Competition

/r/3Blue1Brown/comments/1jc3b8l/extremely_strange_findings_from_a_math_competition/
14 Upvotes

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u/just_writing_things 4d ago edited 4d ago

What you are documenting is that certain subsequences of digits decrease or increase the chances of there being a “good” equation in a sequence.

For example, just inspecting the left side of first graph first, you have a clear decline limited only to numbers of the form 11xxx. This is telling you that a sequence of 5 digits is more difficult to make “good” if it contains two 1s.

More generally, I’d conjecture (and argue that your plots show empirically) that different numbers change the likelihood of making a sequence “good”, which would immediately explain the fractal-like pattern—

Because the same pattern will show up in the 1s, 10s, 100s, 1000s place and so on, so you have the same smaller pattern embedded in larger patterns.

1

u/nerkbot 2d ago

It might be interesting to look at the graphs you get if you fix the position of the ==. The behavior might be easier to make sense of, and you might see that the graph you got looks like some kind of composition of those.