Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

You have 4 machines that are supposed to create 100mg chocolate bars. One of the four machines is not working correctly and is making 90mg chocolate bars. You only have 1 chance to weigh the chocolate bars of 2 of the machines. What is the mathematical equation capable of pulling this off?

share|cite|improve this question
A 100mg chocolate bar wouldn't fill much of a hole. – TonyK Jan 31 '12 at 8:20

I presume you need to find the defective machine?

This seems to be variant of a classic puzzle.

Assume you have a scale which tells you the exact weight and you are allowed to take any amount of bars from each machine. Each machine is supposed to produce 100gm bars, but one of them is defective and produces 90gm bars. In one weighing how do you find the defective machine?

The solution for that is to take one bar from machine one, two from machine two etc and weight the total and consider the difference between the weight you get and the expected total of 1kg.

As to your puzzle, it is not possible to guarantee finding the defective machine in one weighing, if you are only allowed to take bars from two of the four machines.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.