Wolves and sheep












2












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All the sheep were living peacefully in the Land of Shewo. But suddenly they were struck by a danger. A few wolves dressed up as sheep entered the territory of Shewo and started killing the sheep one by one.



To find a solution to this misery, the king of Shewo called upon all of his sheep to the palace hall. He made the following announcement:




From my secret sources, I came to know that the total number of 'sheep' (including the wolves) now present in my kingdom is 100. Among which 5 are wolves. Our doctors have come up with a very expensive blood test which could be used to differentiate the wolves and sheep.



Each test costs 1000$ and we don't have enough funds to test all the 100 'sheep'.



I discussed with our ministers and came to know that the tests can be done on pooled bloodsamples. i.e., I can collect bloods from any number of 'sheep' and mix them. Then if I test the mixture, I will get a positive result if the mixture contain blood from any wolf. I will get a negative result if all the samples are from actual sheep.




One caveat is that the test results are available to you after all the tests are done!




Now , I am looking for ideas where I can find ALL the wolves in minimum number of pooled tests. I request the brilliant young minds of this land to come up with a testing strategy.




Can you help the king by devising a strategy?










share|improve this question









$endgroup$

















    2












    $begingroup$


    All the sheep were living peacefully in the Land of Shewo. But suddenly they were struck by a danger. A few wolves dressed up as sheep entered the territory of Shewo and started killing the sheep one by one.



    To find a solution to this misery, the king of Shewo called upon all of his sheep to the palace hall. He made the following announcement:




    From my secret sources, I came to know that the total number of 'sheep' (including the wolves) now present in my kingdom is 100. Among which 5 are wolves. Our doctors have come up with a very expensive blood test which could be used to differentiate the wolves and sheep.



    Each test costs 1000$ and we don't have enough funds to test all the 100 'sheep'.



    I discussed with our ministers and came to know that the tests can be done on pooled bloodsamples. i.e., I can collect bloods from any number of 'sheep' and mix them. Then if I test the mixture, I will get a positive result if the mixture contain blood from any wolf. I will get a negative result if all the samples are from actual sheep.




    One caveat is that the test results are available to you after all the tests are done!




    Now , I am looking for ideas where I can find ALL the wolves in minimum number of pooled tests. I request the brilliant young minds of this land to come up with a testing strategy.




    Can you help the king by devising a strategy?










    share|improve this question









    $endgroup$















      2












      2








      2





      $begingroup$


      All the sheep were living peacefully in the Land of Shewo. But suddenly they were struck by a danger. A few wolves dressed up as sheep entered the territory of Shewo and started killing the sheep one by one.



      To find a solution to this misery, the king of Shewo called upon all of his sheep to the palace hall. He made the following announcement:




      From my secret sources, I came to know that the total number of 'sheep' (including the wolves) now present in my kingdom is 100. Among which 5 are wolves. Our doctors have come up with a very expensive blood test which could be used to differentiate the wolves and sheep.



      Each test costs 1000$ and we don't have enough funds to test all the 100 'sheep'.



      I discussed with our ministers and came to know that the tests can be done on pooled bloodsamples. i.e., I can collect bloods from any number of 'sheep' and mix them. Then if I test the mixture, I will get a positive result if the mixture contain blood from any wolf. I will get a negative result if all the samples are from actual sheep.




      One caveat is that the test results are available to you after all the tests are done!




      Now , I am looking for ideas where I can find ALL the wolves in minimum number of pooled tests. I request the brilliant young minds of this land to come up with a testing strategy.




      Can you help the king by devising a strategy?










      share|improve this question









      $endgroup$




      All the sheep were living peacefully in the Land of Shewo. But suddenly they were struck by a danger. A few wolves dressed up as sheep entered the territory of Shewo and started killing the sheep one by one.



      To find a solution to this misery, the king of Shewo called upon all of his sheep to the palace hall. He made the following announcement:




      From my secret sources, I came to know that the total number of 'sheep' (including the wolves) now present in my kingdom is 100. Among which 5 are wolves. Our doctors have come up with a very expensive blood test which could be used to differentiate the wolves and sheep.



      Each test costs 1000$ and we don't have enough funds to test all the 100 'sheep'.



      I discussed with our ministers and came to know that the tests can be done on pooled bloodsamples. i.e., I can collect bloods from any number of 'sheep' and mix them. Then if I test the mixture, I will get a positive result if the mixture contain blood from any wolf. I will get a negative result if all the samples are from actual sheep.




      One caveat is that the test results are available to you after all the tests are done!




      Now , I am looking for ideas where I can find ALL the wolves in minimum number of pooled tests. I request the brilliant young minds of this land to come up with a testing strategy.




      Can you help the king by devising a strategy?







      strategy combinatorics algorithm






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 23 mins ago









      Jyotish RobinJyotish Robin

      500112




      500112






















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