I want to tackle them on my free time, BUt I was unable to compete and I really enjoy a good crack from time to time? Can anyone post a link or maybe even the questions themselves? Please no solutions since I want to solve them myself:)
put on hold as off-topic by gnat, MichaelT, Bart van Ingen Schenau, GlenH7, Robert Harvey yesterday
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Well questions of facebook hacker are spread across internet so doing a google search will will give you links to them.
But if you are searching for just problems to solve then the Google Code Jam has Archive of previously Asked Questions.
Also sites like TopCoder and CodeChef have almost Daily or Weekly Contests Also Topcoder have marathon matches which have very tough problems(to burn your Grey cells!!) to be solved in about 7 to 10 days.
If you want more then go to Project Euler.