Deutsche Bank

## Interview Question

Senior Applications Developer Interview

-

# We have a pond containing a single bacterium. The number of bacteria double every 5 minutes, and the pond is full of them in 24 hours. If we started with the same pond but two bacteria, how long will it take to fill the pond?

Tags:logic, algorithm, math

4

I struggled with this a bit and got close. I believe answer is: 23:55

Anonymous on

2

The first pond started with 1 bacterium and doubled to 2 in five minutes. Therefore, the second pond will take 5 minutes less than the first to be full. ie: 23:55

Joe on

1

This is a clear case of Geometric progression. Find the nth term Tn1 = a*r^(n-1). where n = (24 * 60)/5,a = 1 and r=2. when the initial value (a) = 2, the values become n = ?, a = 2 and r = 2. Since Tn1 = Tn2, Equate the RHS of both the equation. Since the base are equal, equate the powers, doing so will give the n value. When n is convert into minutes one get 23 hrs 55 minutes.

Prabhakar on

4

this is easy, you don't need all the math. The pond was half full five minutes before, so it's 23:55

scott on