$interval = <STDIN>; #a number, typically on the order of 500
%HoHoA = (
  'I' => {
     $a => [4,10,200,6000,7000,7100],
     $b => [75,350,5900,6402,7110],
     $c => [0,95,5990,6450] },
  'II' => {
     $a => [lots of numbers],
     $b => [lots of numbers],
     $c => [lots of numbers] },
  'III' => {
     $a => [lots of numbers],
     $b => [lots of numbers],
     $c => [lots of numbers] } );

##</code><code>##

for $RomanNumeral (keys %HoHoA) {   
# For each key RomanNumeral
  for $letter (keys sort {$a <=> $b } %{$HoHoA{$RomanNumeral}} { 
  # The sort will work here, because in this case, the $a, $b, etc are indices
  # For each lettered array in that key
    $i = 0;
    for ($i < length($HoHoA{$RomanNumeral}{$letter})-1) {
      $lowerlimit = $HoHoA{$RomanNumeral}{$letter}[$i];
      $upperlimit = $interval + $lowerlimit;
      #Set a lower limit and an upper limit to the range of numbers we are looking for
        if ($element >= $lowerlimit && $element <= $upperlimit) {
           save $element's value to a new array, keyed by both $RomanNumeral and $letter
          $element here corresponds to all values in the hash %{HoHoA{$RomanNumeral}}, regardless of their $letter key. 
        }
      $i++;
     }
  }

##</code><code>##

$interval = 500;
%HoAoHoA = (
  'I' => [
     {$a => [4,10,200],
      $b => [75,350],
      $c => [0, 95]},

     {$a => [6000],
      $b =[5900],
      $c =>[5990]},

     {$a => [],
      $b =[6402],
      $c =>[6450]},

     {$a => [7000,7100],
      $b =[7110],
      $c =>[]},