Max Word Size as a Function of Number of Words I want to describe the relationship between largest word length, l, and the number of words in a set, n.
Example:


*

*For the set of words {"the", "large", "rock"}, the largest word length is l = 5

*For {"ten", "two", "cat"}, the largest word length is l = 3

*For {"a", "Mathematics"}, the largest word length is l = 11


Can l be approximated as a function of n? How is l related to n?
If n were allowed to be very large, l would obviously be the length of the largest word in the English language. If n were limited to 1, l would obviously be the average size of all words. Intuition tells me that choosing more words gives me a statistically better chance of requiring a more buckets, but I can't explain why.
I am not sure whether this question belongs on StackOverflow or Mathematics. This is not a homework problem. It came up in an answer I posted over on StackOverflow.

Ok, so first of all we have a fixed fnite set of words $A$. To each word there is an associated length. 
for a subset of size $n$ the number of boxes is the maximum value of the length of those $n$ boxes. First of all notice that the relationship depends on the intitial fixed set. (In our case is is the set of words in the english language,so $A$=set of english words).
if we take a set of $n$ letter then the expected value $b$ of buckets is the sum of all of the maximum value of each pair of words divided by the number of pairs of words in the dictionary.
In general for a given $n$ the expected value $l$ of buckets is the sum of the maximum value of all the subsets of $n$ words divided by the number of subsets of $n$ words (denoted $\binom{A}{k}$the size of the set is $\binom{|A|}{k}$).
