A form of the pigeonhole theorem is stated as "If f is a function from a finite set X to a finite set Y with |X| > |Y| then for some ,
Now a question says: An inventory consists of a list of 89 items, each marked "available" or "unavailable". There are 45 available items, show that there are at least two available items in the list exactly 9 items apart.
Now I just don't know how to apply the pigeonhole theorem to this question, what is set X and Y in this case? And what is the function?