Here is a simple solution (unless you are bent on doing it in a longer way using a date time class.)

sub jan1{
 my $y =  shift;
 my $m = 1; $d = 1;
 $m = 11; $y--;
 my $c = int($y / 100); $yy = $y %100;
 my $z = ( 1 + $yy + int($yy/4) + int($c/4) - 2*$c) % 7;
 $z += 7 if $z < 0;
 return $z;   # 0 ==> Sun day.  6 ==> Sat. day.
}

sub sundays{
my $year = shift;
my $j1st = jan1($year);
return 53 if $j1st == 0 || ($j1st == 6 && jan1($year+1) == 1);
       return 52;
}

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