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Paul Evans
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Bob tells the Mr. Sam

that there's a hypothetical computer program called Hyp.
Mr. Sam secretly inputs his number into Hyp. Bob can input two sets into
Hyp. If the secret number is in the first set, Hyp displays a $0$.
If it's in the second set, Hyp displays a $1$. And if it's in neither
Hyp randomly displays either a $0$ or a $1$. Bob's first question is then: "if I input 1 to 9 as the first set and
10 to 18 as the second set, will Hyp display a $0$?"
If Mr. Sam answers "yes" - his number's in the first set, "no" - it's
in the second and "I don't know" - it's in 19 to 27. Bob's second question is: " taking the first 3 numbers as the first set
and the next 3 numbers as the second will Hyp display a 0?" This narrows it down to 3 numbers and the last question uses the first
number as the first set and the next as the second set yielding the
secret number.

Paul Evans
  • 9.4k
  • 2
  • 25
  • 49