## Which box is it?

Here’s a pretty intriguing riddle I came across, which had a pretty awesome solution in my opinion.  The situation is that you have 9 boxes which each have 9 balls.  You know that each ball is 1 kg, but in one of the boxes has balls which have a weight of .99 kg, and you want to find out which box it is.  The catch is that you have a weighing machine, but you can only use it one.  This means that you can find the weight of a set of balls (any number of balls, from any of the boxes, and you can move balls from different boxes) only once.  If you don’t want to see the solution, don’t scroll below the picture.

The solution is pretty ingenious.  Take one ball from the first box, 2 from the next, and so on and 9 from the last.  Now weigh it.  The weight of the balls should be 45 kg, but since some of the balls have less weight, it will be less. How much less?  The amount less that it is will tell you which box is defective.  If there is a deficit of .03 kg, you know 3 balls were defective, so the third box is the one.  I don’t know about you, but this was a pretty cool riddle to me.