I'm not even sure if you simply don't understand or are trolling.
Again: a hash doesn't contain the information to reverse it.
This is not a matter of finding "patterns".
Information that isn't there can not be found.
Thermodynamics / information theory (entropy) is in the way.
I took some time to read some texts related to the subject, and nothing I read said that "information is not there to be found".
Information is there, but highly scrambled.
Some interesting quotes from this
answer (2nd answer on the topic), which is the best I found.
It is unclear whether one-way functions can actually exist. Right now, we have many functions that no one knows how to invert; but this does not mean that they are impossible to invert, in a mathematical sense. Note, though, that it is not proven that one-way functions cannot exist, so hope remains.
There are some functions which can be linked to well-known hard problems. For instance, if n is the product of two big primes, then the function x ⟼ x2 mod n is hard to invert: being able to compute square roots modulo a non-prime integer n (on a general basis) is equivalent to being able to factor n, and that problem is known to be hard. Not proven to be hard, mind you; only that mathematicians have tried to efficiently factor big integers for (at least) the last 2500 years, and although some progress has been made, none of these smart people found a really killer algorithm for that.
This problem is mainly related to
https://en.wikipedia.org/wiki/Integer_factorization where it is very hard to factorize very big subprime numbers. Factorize is to decompose a number into a product of smaller integers.
This was a good example based on the above problem. But it is still reversible, we just don't know how to easily do it.
Let me invent a simple "password hashing algorithm" to show you how it works. Unlike the other examples in this thread, this one is actually viable, if you can live with a few bizarre password restrictions. Your password is two large prime numbers, x and y. For example:
x = 48112959837082048697
y = 54673257461630679457
You can easily write a computer program to calculate xy in O(N^2) time, where N is the number of digits in x and y. (Basically that means that it takes four times as long if the numbers are twice as long. There are faster algorithms, but that's irrelevant.) Store xy in the password database.
x*y = 2630492240413883318777134293253671517529
A child in fifth grade, given enough scratch paper, could figure out that answer. But how do you reverse it? There are many algorithms people have devised for factoring large numbers, but even the best algorithms are slow compared to how quickly you can multiply x by y. And none of those algorithms could be performed by a fifth grader, unless the numbers were very small (e.g., x=3, y=5).
On the post I mentioned on stack exchange he explained how MD5 is hard to invert. It is interesting, and the main problem is related to bit depency, which is :
At that point you begin to understand the problem of inverting MD5: every time you touch a single bit, it triggers an awful lot of modifications throughout the algorithm, which you need to cancel out by touching other bits, and there are just too many interactions. Basically, you juggle with 2128 balls at the same time, and that's way too much to keep track of all of them.
~
So, I looks to be possible. Just not
humanly doable. From time to time even some hash functions are considered broken, just like SHA-1 which became vulnerable to shattred attack (read it here
https://en.wikipedia.org/wiki/Cryptographic_hash_function)
So, personally, I would use your qwk's Planetary Super Efficienty Computer to try to break those hash functions instead of brute forcing them.