A coin is called a Cape Town coin if its value is $1/n$ for some positive integer n. Given a collection of Cape Town coins of total value at most $99+{1\over 2}$ , prove that it is possible to split this collection into at most 100 groups each of total value at most $1$.
I tried it using Pigeon Hole Principle but I'm stuck when making pigeons and holes.
Can anyone help me with this? Or prove that it can't be done in that way.
PS: Please don't miss the emphasized word possible.