Problems
Gary has a large square wall that is exactly 2 × 109 nanometers tall and 2 × 109 nanometers wide. Gary has a dartboard placed on the wall. The dartboard is circular and its radius is between A and B nanometers, inclusive. The dartboard is fully contained within the wall, but it may touch its edges. The center of the dartboard is an integer number of nanometers from each edge of the wall.
Gary invited his friend Mika over to play an interesting game. Gary blindfolds Mika and challenges her to throw a dart at the center of the dartboard. To help her, whenever Mika throws a dart at the wall, Gary will tell her whether the dart hit the dartboard.
Mika does not know where on the wall the dartboard is, but since Mika is very skilled at darts, she can throw darts with nanometer precision. That is, she can aim and hit exactly any point that is an integer number of nanometers away from each edge of the wall. Immediately after throwing each dart, Gary tells her whether she hit the center of the dartboard, some other part of it, or missed it completely and hit the bare wall.
Can you help Mika hit the center of the dartboard, without throwing more than 300 darts?
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