HMMT 2016 U28
- Guts
- Answer
Among citizens of Cambridge there exist 8 different types of blood antigens. In a crowded lecture hall are 256 students, each of whom has a blood type corresponding to a distinct subset of the antigens; the remaining of the antigens are foreign to them. Quito the Mosquito flies around the lecture hall, picks a subset of the students uniformly at random, and bites the chosen students in a random order. After biting a student, Quito stores a bit of any antigens that student had. A student bitten while Quito had blood antigen foreign to him/her will suffer for hours. What is the expected total suffering of all 256 students, in hours?
Dataset text NuminaMath olympiads. Quoted with source.
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\frac{2^{135}-2^{128}+1}{2^{119} \cdot 129}
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