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Falling object collection game

I have a few questions that i need answered or at least a point in the right direction. I have been working on a small game for the iPhone/android that involves catching shapes that fall from the top of the screen that you try to catch in a basket at the bottom. Seems simple enough but I have been having a heck of a time throwing it together, so i will line this out in points.

  1. How can i get randomized shapes to fall from off screen

  2. How can I get those shapes to collide with my basket and recognize what shapes have been collected

  3. How can I get the system to keep track of what shapes have been collected and how many have been collected

Hope I can get some help with this