Problem #WSP-000376

Problem

What is wrong with the following proof that “all rulers have the same length" using induction?

Base case: suppose that we have one ruler, then clearly it clearly has the same length as itself.

Assume that any $n$ rulers have the same length for the induction hypothesis. If we have $n+1$ rulers, the first $n$ ruler have the same length by the induction hypothesis, and the last $n$ rulers have the same length also by induction hypothesis. The last ruler has the same length as the middle $n-1$ rulers, so it also has the same length as the first ruler. This means all $n+1$ rulers have the same length.

By the principle of mathematical induction, all rulers have the same length.