New Jersey Undergraduate Math Competition (NJUMC)

Sample Problems

 

 

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.