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12 balls part 2

You have 12 identical RUBBER balls each of 10 grams and one of 9 grams.You have three weighs of a weighing machine (not a balance scale) to determine which ball is different and whether it is heavier or lighter. Hint: You can do anything with the ball.

See solution

Divide balls into group of 6 and weigh any one group. One group weighs 59 grams.Now divide in group of 3 balls and weigh. One group weighs 29 grams.Now suppose balls A,B and C are left out of which one weighs 9 grams. Now select balls AB and cut any one say ball B into half. Now if 1)ball A is faulty, we will get reading 14 grams.

       2)ball B is faulty we will get reading 14.5 grams.
       3)ball C is faulty we will get reading 15 grams.

**I would like if you can give me some other solution



You can actually do this problem with just a single weigh. You take all of the first ball 1/2 of the second 1/3 of the third 1/4 of the fourth etc all the way to 1/12 of the final ball. The total weight if each ball was 10 grams should 31.032. Then depending on which ball is 9 grams you will be off of that by 1,1/2,1/3,1/4,1/5... etc. So based on the difference between the measured weight and 31.032 you will know which ball was 9 grams. If the ball was 11grams instead then ur just increased instead of decreased.

Anshik Ankit

Another way of solution:

Cut a quarter of each ball, giving us 12 pieces i.e 3 balls. Each piece of quarter should weigh 2.5 grams.

-Weigh any two balls(Attempt one).

  • If two balls (8 pieces) left in doubt. So we weigh any one ball (Attempt two)

  • If one ball left faulty(4 pieces), Cut each of the piece and take 1/2 of the 1st piece 1/4th of second, 1/8th of 3rd and 1/16th of 4th piece. which should give: 1.25, 0.625, 0.3125 and 0.15625. And a faulty one quarter piece(9/4 = 2.24 grams): 1.125, 0.5625, 0.28125 and 0.140625. So by adding the combination we get unique weight and can determine which piece is faulty. (Attempt three)

(Cutting the pieces in half is considerably easy(in absence of any accurate tools), which is why it would be easier to get 1/4th and 1/8th of a piece. And even simplifies the calculations to some extent.)

Shivin Narang

Better solution. there are 12 balls which can be divided in two groups and weigh them. the lighter one contains the 9 gm ball and then pick the lighter one and further divide it into a group of 3 balls. now weigh them lighter one contains the desired ball. now again take the individual ball and weighs two of them if machine is balanced and lighter one in third ball else you got the desired ball. :)

Matt J

Of the last 3 balls left, you don't have to cut one.. Then you would just have a ruined ball. Instead, just place one ball on each side of the weighing machine, while keeping one in your hand or off to the side. If the 2 balls on the machine are equal, then the one in you hand or off to the side weighs 9 grams, otherwise the one on the weighing machine that weighs less than the other weighs 9 grams.

Sachin Rahul

Solution isn't a perfect one. It assumes you find a group weighing 59gms in first iteration. What if you didn't ? There are 13 balls: Two groups of 6 + 1 extra ball. So there is probability that you need to do two weighings to pick group containing lighter ball after diving into groups of 6



there are 12 balls, not 13

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Submitted by
Vishal barot
over 3 years ago
Difficulty 3.3 ?