a) How many different ways can 50 players in a marching band be in rectangle arrangements?
b) If marching bands vary from 21 to 49 players, which number of players can be arranged in the greatest number of rectangles?
For a), I'd take the factors of 50.
1, 50
2, 25
5, 10
Since each of the above can make two different rectangles (1 row with 50 or 50 rows with 1), it looks like the answer is 6.
Sorry, I can't help you with b).