Some explanation of the proposed solutions is in order.

The special variable $. contains a count of the number of lines read from the most recently read filehandle. This number starts with 1. So reading a file line by line, $. will be set to 1, 2, 3, and so on for each respective line read. Read perlvar for details.

This is a convenience, though in this simple case, it's almost as easy to set your own iterator up ahead of time and autoincrement it prior to processing each line read.

The next step is determining even and oddness of a number. One of the easiest ways is to find out the remainder when you divide a number by two. The "remainder" is the modulus of X / 2. And the modulus function is named %. So $x % 2 will be zero for even numbers, and some value for odd numbers. See perlop for more info.

So if you put the two pieces together, and check $. % 2 for value, if it contains any value other than zero, you're looking at an odd line number, and should print that line.

Another solution is to just treat the filehandle as a queue. Instead of shifting one item per loop iteration, shift two, and discard the second, and print the first each time.