The blue-haired wine math puzzle

A king is going to throw a party and has set aside 240 cases of wine. The king’s spies have just discovered that, unfortunately, an anarchist has snuck a substance into one of the cases that will completely and forever turn your hair blue overnight, even if you drink only a drop.

Five loyal dukes have volunteered to try the wine first, and there are only two nights to test as many cases of wine as possible. How many cases can you guarantee are safe? Note that once a duke’s hair has been turned blue, consuming more of the wine has no effect, so he is then useless for further testing.

Give up? The solution is here.

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