Bharat: "Hey, Amar!"
Amar: "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."
Bharat: "Okay! So..."
Amar: "But I will not answer all of your questions. I will leave one question (of my choosing) unanswered."
Bharat: "Oh..."
Amar: "Still want to play?"
Bharat: "Yes!"
So, Amar thinks of a number between 1 and 1000, and Bharat makes up a list of questions.
Amar 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 Bharat.
Now Bharat must guess Amar's number and, if he is wrong, he loses.
How many questions does Bharat need to ask (non-adaptively) in order to correctly identify Amar's number and guarantee a win?
PS: Bharat knows that Amar will be chosing a number between 1 to 1000.