18.314     PROBLEM SET 1    (due September 22, 2005)

Problems 1-7: 
  [Bona] p.11-12 (#17, #18, #22), p. 28 (#18, #20, #23), p. 51 (#28).

Problem 8: Calculate the number of permutations w = (w_1,...,w_{10}) of 
   {1,...,10} such that w_i >= i-2 for all i.  (Here (w_1,...,w_{10}) is 
   a permutation written in the one-line notation.)

Problem 9: Prove by induction that the minimal number of moves needed 
   to move n rings from one spindle to another spindle in 
   the Tower of Hanoi game equals exactly 2^n - 1.

Problem 10:  Find the number of placements of 2n nonattacking rooks
   on the 2n x 2n chessboard such that all rooks stay in white squares.