Secret Santa - Generating 'valid' permutations

Question

My friends invited me home to play the game of Secret Santa, where we are supposed to draw a lot & play the role of \'Santa\' for a friend in the group.

So, we write

Answer 1

In Mathematica you could do something like

secretSanta[n_] := 
  DeleteCases[Permutations[Range[n]], a_ /; Count[a - Range[n], 0] > 0]

where n is the number of people in the pool. Then for example secretSanta[4] returns

{{2, 1, 4, 3}, {2, 3, 4, 1}, {2, 4, 1, 3}, {3, 1, 4, 2}, {3, 4, 1, 2}, 
  {3, 4, 2, 1}, {4, 1, 2, 3}, {4, 3, 1, 2}, {4, 3, 2, 1}}

Edit

It looks like the Combinatorica package in Mathematica actually has a Derangements function, so you could also do something like

Needs["Combinatorica`"]
Derangements[Range[n]]

although on my system Derangements[Range[n]] is about a factor 2 slower than the function above.