If bacteria divided every 20. How long would it take to get 8 bacteria if you started with just 1?

Tricky, tricky …

Let’s see … one division every 20 minutes? That would be like <grinding noise> three binary doublings per hour, right? Now for the tough part … three doublings per hour, for eight straight hours? <more grinding noises> … Is that even mathematically possible? After much thinking, I decide that the total number of binary doublings has to be in the neighborhood of no less than eight times three!

Would you believe that  224=16777216 ? While mathematically true, it is not the answer to the posted question… Since we started at 0 minutes, there are only 23 buddings inside eight hours … so the answer has to be  223=8388608 , right?

Wrong again, this time forgetting all about the newlybud bacteria generations, that all go on budding side by side of their ancestors …

Now that you’ve caught on to the basic idea, I leave it to you to figure out the real answer! Keep in mind that after 20 minutes, you have two budding bacteria to reckon with, for 440 minutes … after 40 minutes another two (for 420 minutes), and so on, down the line.

Hint: the answer still is not 16777216 …

Have fun!