By the way, if you want to guess the number in a guaranteed maximum number of guesses, divide the search space into two instead of randomly guessing.
Change
my $guess = $low + int(rand($range));
to
my $guess = $low + int($range/2);
to see this in action. You'll find the number of guesses is never more than ceil(log2(range)) guesses. This is called a binary search.

ceil(log2(x))
-------------
1..         8:  3
1..        16:  4
1..        32:  5
1..        64:  6
1..       128:  7
1..       256:  8
1..       512:  9
1..      1024: 10
1..        10:  4
1..       100:  7
1..     1,000: 10
1..    10,000: 14
1..   100,000: 17
1.. 1,000,000: 20
1..10,000,000: 24
[download]