Also, your definition of: (define(insert-everywhere/in<blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">-one-word s word)        (cond                [(empty? word)(cons(cons s empty)empty)]                [else(cons(cons s word)                        (insert-middle-end/in-one-word (cons (first word) empty) s (rest word)))]))</blockquote><div> along with its auxiliary function looks overly complicated to me, even if it is a working solution. In the else clause, with the design recipe, before creating auxiliary functions, you should ask yourself if there's some way to assemble the correct answer using the various pieces of the inputs and the recursive call to the function itself.  So, for example, you have the pieces: s (first word) (rest word) (insert-everywhere/in-one-word s (rest word)) Can you combine these elements to solve the answer for the else clause?  That last piece, namely (insert-everywhere/in-one-word s (rest word)), is an important one, and if you can figure out how to use it, your auxiliary function should be simpler and more efficient. --Mark</div>