# How can a Turing machine write the description of the n-th Turing machine?

I am trying to interpret the following problem:

"Describe an algorithm for a Turing machine which receives the integer n as input and proceeds to write the description of the n-th Turing machine from the standard enumeration on its tape."

I am confused about how a Turing machine itself can represent another Turing machine (the n-th Turing machine).

## 1 Answer

The question is probably assuming that there is some arbitrary but agreed-upon convention that specifies how to write a Turing machine description with the symbols of some alphabet. Since all Turing machines have by definition a finite description, all valid outputs will be finite strings.

The exercise itself is an ordinary combinatorics problem.