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Assume I have a list of companies which can be classified according to company type (LLC, LTD), number of employees (0, up to 5, more than 5) and field of operation (Banking, Leisure, Tourism). Every record has a unique identifier.

I should choose a minimum set of companies which fulfills the following criteria:

  • Minimum 10 of every company type
  • Minimum 5 of every employee category
  • Minimum 7 of every field of operation

Now it's clear that the minimum set is determined by the field of operation as 7 x 3 = 21 items. However by cleverly choosing the members of the other category I need not make the set of companies fulfilling all criteria any bigger than 21 (assuming there is any combination which actually fulfills all criteria).

Assume I have 1 million records of companies. How can I determine the minimal sets which fulfill all three criteria?

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