A computer is infected with the Sasser virus. Assume that it infects 20 other computers within 5 minutes; and that these PCs and servers each infect 20 more machines within another five minutes, etc. How long until 100 million computers are infected?

Question

A computer is infected with the Sasser virus.  Assume that it infects 20 other computers within 5 minutes; and that these PCs and servers each infect 20 more machines within another five minutes, etc.  How long until 100 million computers are infected?

rulnick · Answer

20^n=10^8
nlog20=8
n=8/log20=6.15 (approx)
So it will take about 6.15 times 5 minutes, or about 30.74 minutes.
Since the problem says "every five minutes" you may need to round to 35 minutes.