Guess a number part 4. Fill in the blank.

Probability Level 5
  • Bob: "Hey, Alice!"
  • Alice: "Yes, I know. You want to play 'Guess a Number.' I'll play the two-round version where you submit a list of yes/no questions, then I answer them, and then you guess one number."
  • Bob: "Okay! So..."
  • Alice: "But I will not answer all of your questions. I will leave one question (of my choosing) unanswered."
  • Bob: "Oh..."
  • Alice: "Still want to play?"
  • Bob: "Yes!"

So, Alice thinks of a number between 1 and 1000, and Bob makes up a list of questions.

Alice then receives the list, selects one question to leave blank, answers all of the other questions with yes or no, and returns the list to Bob.

Now Bob must guess Alice's number and, if he is wrong, he loses.

How many questions does Bob need to ask (non-adaptively) in order to correctly identify Alice's number and guarantee a win?


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