1. I don't understand the intent of your first sentence here. Are you objecting that the PM solution offered (seems to you) to vary from your instructor's directions? If so, trust choroba's trouble-shooting. Push (see also next graf) allows you to add new elements to an array. When inside a loop, assigning a value to the array REPLACES whatever was in the array on the last iteration of the loop.
2. Perhaps your instructor mentioned using your command line to obtain local help;
   

   C:\> perldoc -f push
   or
   C:\> perldoc -f grep

There are many more sources of help local to your computer. See, for instance, perldoc perldoc and many others.