Another way is to continually adjust the range of acceptable numbers.

As you see, it's often good practice to separate constants at the top of your program so that things can be adjusted easily at a later date.

use strict;
use warnings;

my $min = 1;
my $max = 10;

my $target = $min + int(rand ($max - $min + 1));

print "Please give a number between $min and $max\n";

while () {
    my $guess = <STDIN>;
    chomp $guess;

    if ($guess < $min || $guess > $max) {
        print "Outside of range, please give a number between $min and
+ $max\n";

    } elsif ($guess > $target) {
        $max = $guess - 1;
        print "Too high, please give a number between $min and $max\n"
+;

    } elsif ($guess < $target) {
        $min = $guess + 1;
        print "Too low, please give a number between $min and $max\n";

    } else {
        print "You got the correct number!\n";
        last;
    }
}
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