What is the maximum possible number of different types of prizes?
Explanation:
There is exactly one prize of type a.
As we need to find maximum possible different types of prizes, number of prizes of type b has to be minimum possible and hence must be 2, number of items of type c = 4 …and so on.
1(type a) + 2(type b) + 4(type c) + 8(type d) + 16(type e) + 32(type e) = 63
Suppose there is prize of type f then number of items has to be at least 64. But then there are more than 100 items, which is not true. So there cannot be prize of type f.
Answer: 6.
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