Mrs. Smith gave her children a basket with peanuts, almonds, and cashews. What greatest possible number of nuts in the basket guarantees, that there will be at least one almond and at least one cashew among 100 nuts randomly taken from it? 070-336 exam

(A) 100

(B) 148

(C) 151

(D) 197

(E) 199

maybe A?

A for sure. Easy one

Definitely, if we have 100 nuts, we can guarantee, that at least 1 almond and 1 cashew will be among them. And if we now try to change the question like this:

what is the greatest possible number of nuts, for which there is a possibility, that there will be at least one almond and at least one cashew among any 100 nuts randomly taken from it?

For example, if there are 101 nuts: 30 peanuts, 40 almonds and 41 cashews, we ensure, that no matter which 100 nuts you choose, you will have an almond and a cashew. Is that possible for 199 nuts?