What if we try every possible combination of one-time pads? This is like sculpting with Michelangelo - the correct pattern exists, we just have to remove all of the incorrect patterns from the patternspace.

With one time pads, you can decrypt it to anything, it all depends on the key. See http://en.wikipedia.org/wiki/One-time_pad#Attempt_at_cryptan...

What am I missing here?

So use all keys. Then sort the result and continue to brute-force the correct output.

How many billions of NTLM keys can a Geforce crack in a second? How is this cryptography problem so greatly different than that one?

> How many billions of NTLM keys can a Geforce crack in a second?

According to https://hashcat.net/oclhashcat-plus/ , it's approximately 2.5 B.

This corresponds to a one time pad message of just under 4 bytes long. The difference, of course, with NTLM is you know when you've found the right value. With OTPs, all decryptions are possible and equally valid.

You are missing that when bruteforcing a one time pad you will get all possible arrangements of all letters. How do you tell all the plausible looking strings apart? What kind of a sort function could you apply?