Alien Drugs 2

(If you have not read Alien Drugs 1, please do so here ).

The aliens are back! This time they have engineered another type of drugged candy, in addition to the green and orange varieties. This is the purple candy, which if eaten with the orange one (or vice-versa), cancels out all poisons. But if eaten with a green candy, will immediately result in death. The orange candies have the same effect as they had last time.

They once again find you (how smart are aliens?) and drag you back to their laboratory. Here you see 8 green candies, 1 orange, and 1 purple. The procedure is as follows:

  1. The ten jars and ten candies are placed on a table in front of you.

  2. You are give two minutes to distribute the 10 candies into any amount of jars larger or equal to two.

  3. After two minutes, the empty jars are removed, the remaining jars are mixed around, and you are blindfolded.

  4. You must select two candies from two different jars and eat them at the same time (you have no way of knowing what you have eaten).

The question: What are your best chances of survival? If the answer can be written as A B \frac{A}{B} where A A and B B are coprime positive integers, find A + B + A B A+B+AB .

Bonus: Can you find the grouping method used to achieve this method?


The answer is 41.

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