Bloomberg LP Interview Question Financial Software Developers

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    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.

    - miracle2121 on November 23, 2011 in United States Report Duplicate | Flag
    Bloomberg LP Financial Software Developer Brain Teasers

Country: United States
Interview Type: Phone Interview


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27
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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

- amustea on November 23, 2011 | Flag Reply
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Smart!

- Anonymous on November 23, 2011 | Flag
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Thanks dude, this is the correct answer

- miracle2121 on November 23, 2011 | Flag
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The question specifically states that you don't have a scale.

- Anonymous on November 24, 2011 | Flag
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@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.

- eugene.yarovoi on November 28, 2011 | Flag
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Nice

- SantiagoYMG on December 01, 2011 | Flag
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it is correct

- right on May 29, 2012 | Flag
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a little modification:
take 1 apple from box 1, 2 apples from box 2 ... 9 apples from box 9. That's it.

no need to take any apple from box 10.

- st.jeanbao on April 17, 2014 | Flag
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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!

- kartikaditya on December 01, 2011 | Flag Reply
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should be [{N x (N+1) / 2} - {j x (1 - 0.9)}]

- Polluxgx on February 23, 2013 | Flag
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well done amustea!!!!

- hector on December 17, 2011 | Flag Reply
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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.

- McD on February 08, 2012 | Flag Reply
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What happens if there are less than 55 (1+2+....10) apples in total in all the boxes ?

- Lib Rozario on July 03, 2012 | Flag Reply
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I have 1 solution if it was a weighing scale:
1) Take 1 apple from 1 box
2) Divide 10 apples in 4 groups of 3-3-3-1
3) Check each group on weighing scale
4) It is done in a single step

- Birbal on October 17, 2013 | Flag Reply
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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.

- Lynda T.S. on January 15, 2012 | Flag Reply
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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.

- McD on February 08, 2012 | Flag Reply
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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

- Anonymous on April 04, 2012 | Flag
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what you say is actually 10 steps (sort of smartly merged into one big step )

- amustea on November 23, 2011 | Flag
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the solution should be done in 1 step. in your case it is n number of steps where n is no. of apples

- rob on November 23, 2011 | Flag
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What do you define as a step? Number of movements you make? He has assumed a step means reading once on the digital scale.

- Rayden on November 23, 2011 | Flag
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its really one step :)

- JJJ on January 11, 2012 | Flag
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its really 10 step :(

- jjj on January 11, 2012 | Flag


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