[gpm]

If the data is shorter than the hash shouldn't it be the same data I backed up with reasonably high probability?

[dorgo]

I guess you get (infinite?) many results which all have the same hash and one (or more) of them will be shorter than the hash.

[pathseeker]

No. http://matt.might.net/articles/counting-hash-collisions/

[monktastic1]

Can you explain the relevance? If I put N items randomly into >> N buckets the chance of there being a second item in a particular bucket is small (as opposed to there merely being a bucket with two items, as in the birthday "paradox").

[DuskStar]

That doesn't apply here, since the birthday paradox is about the existence of a collision, not that any particular sequence collides.

Most people in the room will still have unique birthdays even if one pair share theirs.