Learntofish's Blog

A blog about math, physics and computer science

Solution of the 12 balls problem

Posted by Ed on November 30, 2008

Last time I described the 12 balls problem. I also wrote about the 9 balls problem that is easier to solve.

Here is the solution to the 9 balls problem:


Here is the solution to the 12 balls problem:


Now, for the riddle with the 12 balls the trick is the following:
For the first weighing we put 1,2,3,4 on the left hand side and 5,6,7,8 on the right hand side. Suppose 1,2,3,4 goes down as in the picture below. What do you do?


The key step is to put two “heavy” balls on one side and one “light” ball on the other side, e.g. 1,2 on the left and 6 on the right as in the picture below. I leave it to you to find out what you can deduce if the left side goes down.


Besides, I created the pictures with Inkscape, a vector graphics program. I like it very much and it’s freeware.

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One Response to “Solution of the 12 balls problem”

  1. […] come across this problem before, along with some more complex variations. In particular, https://learntofish.wordpress.com/2008/11/30/solution-of-the-12-balls-problem/ already gives a very good explanation of the solution. My only complaint is that I found it a bit […]

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