Learntofish's Blog

A blog about math, physics and computer science

The twelve balls problem

Posted by Ed on November 15, 2008

There are twelve balls that look equal. But one of them has a different weight, though you don’t know whether it is lighter or heavier. Your task is to find that different ball with a beam balance but you are only allowed to use the beam balance three times. How do you do it?

I finally solved the ‘twelve balls riddle’. It took me 3 months. Of course, as you can guess from the time this problem kept me busy, I found it quite hard. I learned something from it: if you really want to solve a problem sit down, take paper and pencil and work seriously on it. When I worked on the twelve balls riddle I often sat in the train trying to solve it in my head. But even when I had something to write on I was often too tired. Moreover, you can imagine it is not particularly comfortable writing down things in a train.
So what I mean with
seriously is that you should put all your effort into solving the problem. Create the best possible conditions that you can work under, e.g. by having a large and clean desktop. Work in a calm environment such as a library. And work with a clear mind and not when you are tired. Do not make it any harder than necessary by trying to imagine the solution solely in your head instead of using a notepad.
And guess what: when I finally found the solution, I was at home with paper and pencil.

If you like to solve the ‘twelve balls problem’ I recommend having a look at the ‘nine balls problem‘ first. It is much easier:
There are nine balls that look equal. But one of them is heavier. How do you find the heavier ball by using a beam balance only twice?
Note that this time you know that the different ball is heavier and that you can use the beam balance only twice.

I will post my solution to both problems later.


2 Responses to “The twelve balls problem”

  1. […] by Ed on December 8, 2008 Last time I posted my solution for the 12 balls problem. However, I discovered on one of my scratch papers […]

  2. […] comments Solution of the 12 b… on The twelve balls problem3d cameras – H… on Motion Control – Sony an…Ed on Nice Introduction to […]

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