Since the year 2000 is a leap year and 29th February falls on a Tuesday, it means that in the 4 years of this leap year cycle, there will be 1 occurrence of 29th February falling on a Tuesday.

A leap year occurs every 4 years, except for years that are divisible by 100 but not by 400. Since we are considering a whole century starting from 2000, we need to count the number of leap year cycles in this century.

There are a total of 25 leap year cycles in a century (100 years divided by 4 years per cycle).

In each leap year cycle, there is 1 occurrence of 29th February falling on a Tuesday. Therefore, in the whole century, 29th February falls on Tuesday 25 times.

So, the correct answer should be option 2: 4.

Alert - correct answer should be option 2: 4.