How to verify new digits of $\pi$?

algorithms pi

Solution 1:

Since you allow any base, (16 in particular) and randomized algorithm, you can use the Bailey-Borwein-Plouffe formula which allows you to compute the $n^{th}$ digit of $\pi$, without having to compute the earlier $n-1$ digits! (Alas, such a algorithm seems to have been discovered only for base-16.)

All Alice needs to do is pick "some" random digits and compare.

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