Cracking a PRNG by observing ranks within groups of its output
Assuming $w=32$ (32-bit integers for internal state), $624 * 32 = 19968$ bits of information is found in the internal state. On the other hand, a maximum of $\lfloor\log_2(100!)\rfloor=524$ bits of information is revealed by each ranking of 100 outputs. $\lceil19968/524\rceil=39$ rankings of 100 outputs each would be the minimum information I would expect to need to identify the state. I do not, however, know of an algorithm to use the revealed ranking information to calculate the state.

You talk about "leaking" information and ask about a "cracking process". I hope you are not attempting to use a Mersenne Twister when a cryptographically secure pseudo-random number generator is needed.