Instructions

Use recursion to write a function is_sorted that consumes a list of numbers and produces True if the items in the list appear in sorted order and False otherwise. A list of length zero or one is always in sorted order.

Use recursion to write a function all_equal that consumes a list of numbers and produces True if all the items in the list are equal and False otherwise. An input of a list of length zero or one will produce True.

Use recursion to write a function divides_all that consumes a list of positive integers seq and a positive integer factor. Your function should produce True if every item in seq is a multiple of factor and False otherwise. The helper function is_multiple has been provided for you.

Use recursion to write a function contains that consumes a list seq and a value item. Your function should produce True if item is an element of seq and False otherwise.

Do not use the built-in function in.

Use recursion to write a function reverse that consumes a list seq and produces a new list with the same items as seq but in reverse order. A list of length zero or one is its own reverse.

Use recursion to write a function multisplit that consumes two positive integers total and split and produces the number of times total is repeatedly divided into split even pieces before each piece is of size at most 1.

For example, the value returned by multisplit(8, 2) will be 3, since 8 can be split into 2 pieces of size 4, which are then each split into 2 pieces of size 2, which are then each split into 2 pieces of size 1 (at which point no further splitting takes place since the pieces are of size at most 1). The value returned by multisplit(8, 3) will be 2, since 8 can be split into 3 pieces of size 8/3, which are then each split into 3 pieces of size 8/9 (at which point no further splitting takes place since the pieces are of size at most 1).