Fun exercise. So, I will take the challenge.
Now, I'll take a stab at this without doing any cheating. Then I will check my work and place it below in an 'update'.

First, my guess...

my $i = 0;             # init $i and set to 0

print ++$i + 1;        # answer: 1 (0 + 1) post-operation -> $i == 1 n
+ow
print $i++ + 1;        # answer: 3 (2 + 1) post-operation -> $i == 2 n
+ow
print $i + $i++;       # answer: 5 (2 + 3) post-operation -> $i == 3 n
+ow
print ++$i + ++$i;     # answer: 7 (3 + 4) post-operation -> $i == 7 n
+ow
print ++$i + $i++ + 1; # answer: 17 (7 + 9 + 1) post-operation -> $i =
+= 17 now
[download]

Update:

Looks like I was way off :(

perl -Mstrict -e '
my $i = 0;  

print ++$i + 1,"\n"; 
print $i++ + 1,"\n";     
print $i + $i++,"\n";  
print ++$i + ++$i,"\n"; 
print ++$i + $i++ + 1,"\n";
'
2
2
5
10
14
[download]

It looks like I had my pre- and post- backwards. Dumb mistake, really. I seem to have been making a lot of those lately. However, I did enjoy this little exercise.

_ _ _ _ _ _ _ _ _ _
- Jim
Insert clever comment here...