Do all finite digit strings occur in pi?

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Izzhov
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Is there a proof or disproof that any given finite string of digits will occur somewhere in Pi?
 
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No, there isn't. That would be equivalent, I think, to saying that [itex]\pi[/itex] is a "normal number" and that has not been proved or disproved.
 
It smells equivalent to the property of normalness, but I'm not sure if it is easy to prove..