Examples of mathematical induction What are the best examples of mathematical induction available at the secondary-school level---totally elementary---that do not involve expressions of the form $\bullet+\cdots\cdots\cdots+\bullet$ where the number of terms depends on $n$ and you're doing induction on $n$?
Postscript three years later: I see that I phrased this last part in a somewhat clunky way. I'll leave it there but rephrase it here:



--- that are not instances of induction on the number of terms in a sum?




Suppose that in a group of $2n + 1$ people, for every group of $n$ people there exists one person (which is not one of them) who knows each of them. Here the relation "knows" is symmetric.
Then, there exists one person who knows all the other $2n$ people.
