Blackboards

Author: munch

The integers from 1 to 99 have been written on a blackboard. We define an operation on any a, b, and c in the board that replaces the three numbers with the number abc+ab+ac+bc+a+b+c.

Munch applies this operations some number of times, until the only number remaining on the board is x. How many trailing zeros does x+1 have? For example, if x = 1101022999, there would be 3 trailing zeroes.