KeyGenMe #4 :: C++ :: Difficulty : 4 [HARD !]

KeyGenMe Location : KeyGenMe #4 @ Crackmes.de
Solution Location : Not Solved Yet.

My hardest KeyGenMe yet !! KeyGenMe #4. It's coded in ANSI C++. Features :
(*) NOT Packed
(*) NOT Encrypted

The Rules :
(*) NO Patching
(*) NO Brute-forcing

The Tasks :
1. Try to get Status as "VALID :) !".
2. Find the algorithm for the computations involved.
3. Make keygen to VALID Key for ANY name. Please note that VALID KEYS EXIST FOR ALL NAMES.
4. Write a descent tutorial. ;)

The Hint :
==========---
Think about solving a 15-puzzle. ;)

Readers, if you solve this, please upload your solution to CrackMes.de.