(Solved) : Certain Friend Mine Spent Better Part Lifetime Testing Recreational Drugs Thorough Testing Q43913382 . . .
A certain friend of mine has spent the better part of a lifetimetesting recreational drugs. After thorough testing, this friend hasidentified 20 recreational drugs D1,…,D20 and determined(experimentally) that any 3 of these drugs can be takensimultaneously with no adverse effects.
- Assuming my friend determined this entirely by testing, howmany experiments did my friend have to perform?
- A new designer drug called D21 has just hit the streets and myfriend wants to know if D21 can be added to their list. That is,can any triple of D1,…,D21 be safely taken together? How manyadditional experiments does my friend need to determinethis?
- Suppose my friend survives the experience and D21 makes it ontothe list. My friend takes scrupulous notes about all experimentsand notices something peculiar about the answers to the precedingtwo questions. What combinatorial identity did my friend justdiscover?
- Suppose that an impatient novice wants to repeat my friendsdiscovery using fewer experiments. This novice is willing to take 5drugs at a time. What is the fewest number of experiments thisnovice can perform so that for any triple Di,Dj,Dk∈{D1,…,D21}, atleast one of this novice’s experiments includes Di, Dj, andDk?
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