1. What is the probability that a dart, hitting a square board at random, lands nearer the center than the edge?
2. Call a number N fortunate if it can be written with four equal digits in some integral base b>1. (a) Clearly 2222 is fortunate; why is 2000 fortunate? (b) Find the greatest fortunate number less than 2000.
3. Determine whether converges or diverges.