How to find max number with a single-tape turing machine?
There are many ways to tackle this. This is just one suggestion. I assume you need a single-tape machine, and that you actually need to write it down formally, so you need a very simple solution, not something like "just compare the numbers".

Start by finding $\max\{x_1,x_2\}$, and replacing $x_1,x_2$ with this new number. To do this, you can take to new symbols $X,Y$, and erase one letter from each number using one of $X,Y$. After one of the numbers is erased, you remain with the second number. You can then erase the smaller number, and restore the bigger one to $1$'s.

Then, simply repeat the process until you are left with a single number.
It requires several states, but it shouldn't be too huge.