The importance of visualization in problem solving

Written on 10 February 2019, 12:36pm

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This weekend I thought about the flashlight and 8 batteries riddle:

You have a flashlight that works with 2 batteries. You also have 8 batteries, of which 4 are empty and the other 4 are full. There is no way to tell which battery is empty and which one is full, but you can put 2 batteries in the flashlights. If both of them are full, the flashlight will turn on.

What is the minimum number of tries that will guarantee that the flashlight will turn on?

At first, I explored the possible combinations, then I considered playing with probability trees. But then I put this on paper, and soon, things became much clearer. I represented the batteries with dots, and the tries with lines, and instead of playing with abstract concepts, I started to play with lines and dots:

Dots and lines

First I found a solution that would try 7 combinations, and would guarantee that the 8th was correct:

8 lines, guaranteed to work. But could it be better?

But somehow I knew that the solution had to be 7 tries, not 8. So I kept moving the lines and connecting the dots until the bulb lit (pun intended):

The solution: it had to be symmetric…

No matter where the 8th full battery is, there will be a line connecting it with another full battery. (You can also find a video here).

This shows the importance of visualizing your problem before being able to come up with the answer. I am using a Moleskine notebook and a Baron Fig Squire pen (some say it’s the best pen in the world 🙂 ).

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