This was a relatively difficult puzzle for many children, and I did not get too many responses. The only correct answer amongst the younger lot came from Smiti Mittal – congrats Smiti! I also got a correct answer from Ruchir, and a couple of other people threatened me with a correct answer, but did could not send it J
Here is the correct answer (Sorry no video this time, traveling currently without an iPad):
First balance a red and white ball against a blue and a white ball. If the scales balance, you know that there is a heavy and a light ball on each side. One can then weight the two whites against each other to figure out which is the heavier and lighter one. This in turn will help you determine the lighter and heavier ones for red and blue balls as well by keeping track of the ones you used in the first weighing.
If the two sides do not match in the first weighing, one should be able to quickly realize that the heavier white lies on the side of the heavier side of the balance. For the sake of simplicity, let’s assume that the red lies on the lighter side of the scale and therefore blue lies on the heavier side of scale. For the next weighing, put the original red on one side against the blue that was not used in the first weighing.
If they match, then the original red and the blue used in the second weighing are both light.
If they do not, then one can anyway figure out the lighter and the heavier ones amongst the reds and blues.
Hope you enjoyed the puzzle!