## Interview Question

Enterprise Architect Interview

-Manchester, NH

# Having and scale and 9 equally shape and color with only one being slightly heavier than the rest, find the heavier ball with minimum number of interactions.

Tags:brain teaser

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The solution is to divide in 3 groups of 3 balls each and and weight them.

Anonymous on

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took me 20 seconds to solve. Divide the 9 into 2 groups of 4 and one aside. If the weight is the same for the 2 of 4 the one out is the heavier. If one group of 4 is heavier you know that one group has the heavier element. Divide that 4 into 2 of 2 and measure again. The heavier group of 2 has the heavier element. Measure each one now.

Fausto on

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Correction to my solution.The last step only measure ONE of the two. The weight should be 1/4 of the group of 4. So this eliminates the need to do 2 more measures. So total we will have either 1 measure only because the one left out of the first measurement was the heaviest OR 3 to find final.

Fausto on

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Even faster solution because of the statistics: measure one group of 3 and another group of 3. You will find out either the weight of 1/3 for a block or which one is heavier than the other group. If both first groups of 3 are the same weight, the last group of 3 has it, otherwise one of those 2 first groups has the heaviest. Take the heaviest group of 3. You know now the weight of each block by simply dividing the found weight of the first lighter group of 3 divided by 3. Now take the remaining (or found heaviest group of 3) and divide onto one group of 2. If the weight is 2/3 of the unit the left out is the heaviest, so total of only 2 measures so far, BUT if the weight of those 2 is greater than 2/3 you know one of those is the heaviest so you need one more measure only.

Fausto on