1. countdown Example: countdown(5,[5,4,3,2,1]).

 NOTE - your function should be able to answer questions such as: ?- countdown(5,L).

 2. count_occur Example: count_occur(7,[5,2,6,7,8,7,0],2).

 the list [5,2,6,7,8,7,0] has 2 occurences of 7

 3. array insert Example: ains([0,0,1,1,2,2],4,53,[0,0,1,1,53,2,2]).

 and array get Example: aget([0,0,1,1,53,2,2],4,53).

 These functions simulate array operations, using lists.  "ains" takes a list, an index, and a value to insert, and produces a list with the value inserted at the index point.  "aget" takes a list and an index, and produces the value from the list at the index point.