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A spy is located on a one-dimensional line. At time , the spy is at location . With each time interval, the spy moves units to the right (if is negative, the spy is moving left). and are fixed integers, but they are unknown to you. You are to catch the spy.
The means by which you can attempt to do that is: at each time interval (starting at time ), you can choose a location on the line and ask whether or not the spy is currently at that location. That is, you will ask a question like "Is the spy currently at location ?" and you will get a yes/no answer. Is it possible to guarantee that you find the spy after finitely many questions?