The refresh issue can be fixed by slightly modifying the following:

my $screen = $top -> Label(
    -textvariable => "$number",
    -background => 'white',
    -width => 30,
    -borderwidth => 2,
    -relief => 'sunken',
) -> pack(-pady => 5);
[download]

To:

my $screen = $top -> Label(
    -text => \$number,
    -background => 'white',
    -width => 30,
    -borderwidth => 2,
    -relief => 'sunken',
) -> pack(-pady => 5);
[download]

There are other issues with the logic you're using for the numbers. Still, it's a pretty good first attempt.

Rob