while ($Input = <IN>) {
  if ($Input !~ /^Answer/) {
     if ($Input =~ /^(\d+)/) {
        $Number = $1;
     }
     print QUESTION "$Input";
  }
  else {
     print ANSWER "$Number $Input";
  }
}
[download]

If things get any worse, I'll have to ask you to stop helping me.

Okay, I'd attack this with a few regexps. I'd have two output files concurrently open, one to answers.txt and one to questions.txt (or whatever), and simply while(<>) through the input file..

The first regexp checks if the line starts with a series of digits, if it does then assume it's the question number and store it for later.

The second regexp checks if the line begins with the word 'Answer', if it does then it prints out question number and this line to answers.txt, otherwise it prints out current line to questions.txt.

Not quite pseudocode, but should be enough to go on!

# Read input a paragraph at a time
# and put carriage returns on output lines
local $/ = "\n\n";
local $\ = "\n";

# Read input, one question at a time
while (<>) {
  chomp;

  # Grab the question number
  my $number = /^(\d+\.)/;

  # Split the question into lines
  my @question = split /\n/;

  # The answer is the last line
  my $answer = pop @question;

  # Send the results to different output streams
  print OUT1 join("\n", @question);
  print OUT2 "$number $answer";
}
[download]

buckaduck

#untested 

open(QUESTIONS,">$questions") or die $!;
open(ANSWERS,">$answers") or die $!; 
open(READ_FILE,"$read_file) or die $!;

my($answer,$number);
while(<READ_FILE>) {
    if($_ =~ /^(\d+)/) {
        $number = $1;
    }
    if($_ =~ /^Answer: (\w)/) {
        $answer = $1;
        # print the last number found
        print ANSWERS "$number. Answer: $answer\n";
    }
    else {
        print QUESTIONS $_;
    }
}
close(ANSWERS);
close(QUESTIONS);
close(READ_FILE);
[download]