Solve the N Queens problem two different ways.

Still submit them as a single word document, but keep them
clearly delineated.

Best: three clearly separated regions, first containing those
   things common to both solutions, second containing those
   things only used for the first, third containing those
   things only used for the second.
Good enough: two clearly separated regions, first containing
   everything for the first solution, second containing
   everything for the second.

Test runs for both as always.

Method 1: ordinary depth-first search with whatever you need
  to make it work effectively. If you want a closed set you
  can have one, etc. Simply inserting the Queens in columns from
  left to right, only adding a new Queen after making sure she
  is not under attack and backtracking when it is impossible
  to put a Queen in a column is good enough (provided you make 
  it work)

Method 2: best first search. The following is only a suggestion,
  I'm hoping that seeing it might help you to see something
  better. You could just pick a number of unoccupied squares
  (all of them for true best first, but fewer might be more
  interesting and sustainable) apply a measure of performance
  to each and add non-failures to the priority queue. Measure
  of performance: I'm sure you can think of many, proportion
  of unoccupied squares that are not under attack is worth
  a try. Unless you can somehow come up with a perfect measure
  of performance (next state with best score is guaranteed to
  lead to success) backtracking will still be needed here.
  That could be a lot easier than it sounds.

There will be further discussion of this on Monday 17th, but that
doesn't mean you should wait until then, you've got the essentials,
I just want to deliver an extra clue. You'll be happier if you
come up with it yourself before then.

If you are unsure about the chess rules for Queens attacking other
pieces, the queen-attacks.pdf link in Wednesday's material shows
you them.