36! includes factors of 25, 30 and 35 not found in 24! and therefore its prime factorization has four more 5's, and therefore the number itself has four more terminal zeros.
As a result, the answer should depend only on 24!, by subtracting the last two digits before the terminal zeros, from 100. Hopefully the first of these is not a zero itself--nothing prevents internal zeros.
Posted by Charlie
on 2014-01-12 12:19:41