Curious Consecutive Cyphers (Posted on 2008-11-25)

Each of the last T digits in the decimal representation of the product of 1!*2!*3!.....99!*100! is zero, but the (T+1)^{th} digit from the right is nonzero.

Determine the remainder when T is divided by 1000.

Note: Try to derive a non computer-assisted method, although computer program/spreadsheet solutions are welcome.