[Guest]

There are ten pills (tablets) producing machines in a factory. One of them is faulty. The faulty machine only makes pills one gram less than the actual weight, which is 10grm (correct weight). You have a weighing machine in the room as well. Your job is to find out the faulty machine in the room. But there is a condition:

• You only allowed to use the weighing machine once.

How to spot the faulty machine?

The answer is very simple. Make one pill from first machine then two pills from second machine and so on. Total number of pills is

n(n+1)/2 , which is 10(10+1)/2 = 55

Total weight of 55 pills (assuming all ten machines are working properly) = 550grms

Put all 55 pills on the weighing machine to get the weight.

If weighing machine only shows the total weight as 549grms, the first machine is faulty as we only made one tablet from it. If the total weight is 548grm, it’s clear that the second machine is faulty because we made two tablets from it.

[Guest]

You take 1 pill from the 1st machine, 2 from second and so on. You'll get 55 pills which should weigh 550 g if all the machines were correct. But since one of the machines is faulty, the actual weight would be lesser. And the difference in actual weight with ideal one will tell which machine produces the faulty tablet.

For eg. If machine 6 produces 9g tablets, then the actual weight of 55 tablets would be 544 grams.

[Guest]

yes you are right.