## Bloomberg LP Interview Question Financial Software Developers

• 0

There are 10 boxes of apples. Each apple in the boxes weights 1 pound, except that one of the boxes contains bad apples, which weights 0.9 pound each. You are given a digital weight (not a scale), and you can take apples out of the boxes. what is the minimum time of weighs to find out which box has bad apples?
I gave one solution of 3 times using divide and conquer, but the interviewer said that 1 step is possible. So I couldn`t come up with the solution.

Country: United States
Interview Type: Phone Interview

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23
of 23 vote

it's simple:
take 1 apple from box 1, 2 apples from box 2 ... 10 apples from box 10

put all on scale, say it shows XX.Y pounds
look at Y (fractional part).
if it's 0, it's box 10
1 - box 9
2 - box 8
...
9 - box 1

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0

Smart!

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0

Thanks dude, this is the correct answer

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0

The question specifically states that you don't have a scale.

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0

@Second Anonymous: he meant "digital weight". There is no comparison of weights, only an absolute number, so this solution is correct.

This is probably not the only possible correct solution, but it certainly is correct.

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0

Nice

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0

it is correct

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0
of 0 vote

``````Assign a number to every box say 1-N.
Take i apples from box i for measurement.
You will end up in [{N x (N+1) / 2} - {j x 0.9}] pounds.
Since you know N, calculate for j, which is the faulty box!``````

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0

should be [{N x (N+1) / 2} - {j x (1 - 0.9)}]

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0
of 0 vote

well done amustea!!!!

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0
of 0 vote

One step solution:
1. Label boxes 1- 10.
2. Pick 1 apple from 1st box, 2 apples from 2nd box,.....10 apples from 10th box.
3. If all were good, their weight should add up to 1^2 + 2^2 + .....+10^2 = n.(n+1).(2n+1)/6 = 385.
4. Now measure the actual weight A.
5. (385 - A)*10 is your answer.

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0
of 0 vote

What happens if there are less than 55 (1+2+....10) apples in total in all the boxes ?

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-1
of 1 vote

Scrutinize all the other apples in all the boxes.The bad apples might look bad, smaller, wrinkled, smell off, dark patches ... pick the worst looking one from that box that look "terrible" and another from any box, that looks OK. Feel them (to be convinced) and weigh the one that looks bad. Use all the senses to judge, and the scale to verify.

We are comparing apples to apples and a tenth of a pound off is not negligible.

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-1
of 1 vote

One step solution:
1. Label boxes 1- 10.
2. Pick 1 apple from 1st box, 2 apples from 2nd box,.....10 apples from 10th box.
3. If all were good, their weight should add up to 1^2 + 2^2 + .....+10^2 = n.(n+1).(2n+1)/6 = 385.
4. Now measure the actual weight A.
5. (385 - A)*10 is your answer.

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0

If all were good, their weight should be 1+2+3+4+5+6+7+8+9+10=55

Thus should be (55-A)*10

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0

what you say is actually 10 steps (sort of smartly merged into one big step )

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0

the solution should be done in 1 step. in your case it is n number of steps where n is no. of apples

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0

What do you define as a step? Number of movements you make? He has assumed a step means reading once on the digital scale.

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0

its really one step :)

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0

its really 10 step :(

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