Generate lists with exactly one item in common
<p>In Python, I'm poking around with an idea but I'm not exactly sure how to implement it correctly.</p>

<p>I have a pool of 26 letters ('A' - 'Z'), and each letter can be used as many times as needed. I want to create lists using these letters; each list will be 10 letters long with no repeats inside them, and I want to guarantee that if I compare any two lists generated, there will be <em>exactly one</em> letter in common.</p>

<p>Questions:</p>

<ul>
<li>Is there a simple way to do this (i.e., by using library functions)?</li>
<li>Can I calculate the maximum number of lists I'll be able to create given the size of the pool (pool_size) and the length of the list (list_length)? </li>
</ul>

<p>Any pointers to relevant material would be appreciated; I don't need an implementation so much as somewhere to lay my Archimedean lever (to be read as: I need a foundation before I can build my idea).</p>

<p>"Give me a place to stand on, and I will move the earth." - Archimedes</p>

<p><strong>UPDATE</strong>: How naive of me to think that the alphabet was enough to work with. Let's expand the pool to 300 symbols, but keep the lists at length 10. Does that work?</p>
