The trick to seeing why it's on page 314 is to note that the spacing on the sentence is really odd. Since spaces are significant to the algorithm, the same words with different whitespace will end up on different pages of different books.

From the information on https://libraryofbabel.info/referencehex.html, we can see that each book has exactly 410 pages. Assuming that for any phrase X, the page that that phrase is on is independent and equally likely, then there is a 1/410 chance that the phrased being searched will be on page 314. So just write a script that hits libraryofbabel.info automatically with randomized spacing. You'll likely end up on a page that is 314 in about 410 or so tries.

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