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Problem of the Month – July, August 2017

There are 2017 nonempty bags each containing finite number of colored balls. Find the smallest value of k for which no matter how the contents of bags are arranged the bags can be distributed into k boxes so that for each box at least one of the following two conditions is held:
• all bags of a box contain a ball of the same color
•• each bag of a box contains a ball colored differently from all balls of all other bags of this box.