Mathfag here, that's actually not known. It's conjectured that every possible combination of digits appears in pi's decimal expansion (that's called being a "normal" number), but it hasn't been proven, and it doesn't follow from the fact that it's infinite and nonrepeating. And to the people saying certain number combinations are impossible: no they're not, they're just unlikely.
i can't supply a proof but i would venture a guess that certain number combinations are impossible. for example, 50,000,000 zeroes side by side. There may be a proof out there that shows that numbers cannot repeat past a certain amount due to the nature of the calculation. idk for sure though
The string 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 did not occur in the first 200000000 digits of pi after position 0.
(Sorry! Don't give up, Pi contains lots of other cool strings.)
doesn't mean it doesn't exist...but there may be a proof along the lines of Fermat that shows for the calculation of pi using an n-gon with n approaching infinity, since it involves square roots, that no set of consecutive square roots can be summed to give a string of 'x' zeroes.
like i said, such a proof may not exist, but if it did my guess is it would look something like that
the first time 3 digits in a row are the same number doesn't happen until about 160 digits, it doesn't seem like a number that likes repeating numbers.
every time i see this picture, im amazed at how much that guy looks exactly like one of my friends. first time i saw it, i actually thought it was him.
then i looked down and saw he's doing homework and i no longer believed such silly things