Which company is faulty?

Level pending

There are 9 bags of balls of 9 different companies. If all of the companies make identical (in each aspect) balls, each weighing 20 units, but 1 of the company makes faulty balls of lesser weight, and you have as many balls as you want of each company, and a weighing machine. A "weighing of the balls" refers to measuring the total weight of any combination of balls from the companies. What is the minimum number of weighings that are needed to determine the faulty company?


The answer is 1.

Payal Sheth by Payal Sheth , 22, India

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2 solutions

Payal Sheth
Jul 5, 2014

Take 1 ball of the 1st company, 2 of the 2nd, 3 of the 3rd and so on. Weigh them. Now, just take that number and you can use algebra and see which one is faulty.

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that still not 1 times :P

Hafizh Ahsan Permana - 6 years, 11 months ago

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weigh them together.. And if all companies were producing ideal balls of weight 20 units, the total weight would have been 20(1) + 20(2) + 20(3) and so on till 20(9) You have to just calculate this total weight and you'll get the answer by using algebra.

Payal Sheth - 6 years, 11 months ago

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This will not necessarily help, if we don't know how much the lighter balls weigh! For example, the total weight if they were all 20 unites would be 45(20)= 900. Say we weighed using the method above and achieved a weight of 850, a 50 unit deficit. Well, this could be 5 balls that are 10 units lighter, 4 that are 12.5 units lighter, etc. Your method does not guarantee results!

Nicolas Bryenton - 6 years, 10 months ago

Ya but how you will be able to identify the ball that has less weight ! :?

Ishan Kothari - 6 years, 10 months ago

consider ist we are taking 9 balls each of different companies we divide them into two groups containing 4 balls each thus leaving aside 1 ball . If the weight of both groups are equal then the one taken aside is of differential weight, and the question is asking about minimum number of weighings which =1

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