Lets take a slightly different version of the faulty balls – You have multiple machines producing table tennis balls. Each ball is supposed to weigh 10 grams. One of the machines is faulty and is producing balls of either 9 grams or 11 grams, i.e. it is off by 1 gram. You have a very accurate digital weighing machine which will tell you the weight in grams of whatever you put into it.
1. (For children up to 12 years) – Assume you have only 3 machines, and are allowed only one weighing. How will you identify the faulty machine.
2. (for children above 12 years) – Assume you have 10 machines, and again are allowed only one weighing. How will you identify the faulty machine.
3. (For high schoolers and adults) – Now there is a twist in the problem – the faulty machine is off by either 1 gram or 2 grams, i.e. it produces balls of one of the following weights (in grams) – 8, 9, 11, or 12. We do not know which one is the case. Again, you can do only one weighing. What is the minimum number of balls you will need to weigh to arrive at the answer for the faulty machine (and how many grams is it faulty by).
Last part of the question was created with some friends on a trek last year around 6 months back to whom credit is due – Alok Mittal, Parul Mittal, Neeraj Aggarwal, Aman Singla & Naresh Kumra.