The particular cultivar of raspberries in my garden has between 100 and 125 drupelets per berry. Each cane produces at least 55 berries. Does each cane produce at least two berries that have the same...

The particular cultivar of raspberries in my garden has between 100 and 125 drupelets per berry. Each cane produces at least 55 berries. Does each cane produce at least two berries that have the same number of drupelets? Use the Pigeon Hole Principle to construct an argument that supports your answer.

Assume that a and b are integers where
   and both S and T are sequences on R.

(a) Explain why

(b) Explain why
  for any number c.