#!c:\perl\bin\perl.exe
#
# FILE:  autoprime.pl
#
# Daruma
# 09-MAY-2003
#
# puzzle:  What 5 digit number am I thinking of?
#   It has 2 prime digits.
#   Digit 3 is the highest number.
#   Digit 2 is lowest.
#   Digit 5 is between digit 2 and digit 1 and is half of digit 4.
#   There are no duplicates.
#   Digit 1 is 1 less than digit 3.
#   Digit 1 is higher than the sum of digits 4 and 5.

use warnings;
use strict;

my $candidate;
my @digits;
my $flag;

for ($candidate = 12345;
     $candidate <= 98765;
     $candidate++) {
       $flag = 0;
       check_prime($candidate);
       check_digit_3($candidate);
       check_digit_2($candidate);
       check_digit_5($candidate);
       #check_duplicates($candidate); # problem?
       check_digit_1($candidate);
       if ($flag < 1) {
	 print "$candidate\n";
       }
}

# subroutines

sub check_prime {
  # The candidate number must have 2 prime digits
  my $candidate = shift;
  my @digits = split //,$candidate;
  my $prime_count = 0;
  foreach my $digit (@digits) {
    if ($digit =~ /(2|3|5|7)/)  { $prime_count++ }
  }
  if ($prime_count != 2) { $flag++ }
}

sub check_digit_3 {
  # Digit 3 is the highest number.
  my $candidate = shift;
  my @digits = split //,$candidate;
  my $digit_3 = splice @digits,2,1;
  foreach my $digit (@digits) {
    if ($digit_3 < $digit) { $flag++ }
  }
}

sub check_digit_2 {
  # Digit 2 is lowest.
  my $candidate = shift;
  my @digits = split //,$candidate;
  my $digit_2 = splice @digits,1,1;
  foreach my $digit (@digits) {
    if ($digit_2 > $digit) { $flag++ }
  }
}

sub check_digit_5 {
  # Digit 5 is between digit 2 and digit 1
  # and is half of digit 4.
  my $candidate = shift;
  my @digits = split //,$candidate;
  my $digit_5 = pop(@digits);
  my $digit_1 = shift(@digits);
  my $digit_2 = shift(@digits);
  my $digit_4 = pop(@digits);
  if ($digit_5 > $digit_1 and $digit_5 < $digit_2) {} # good
    elsif ($digit_5 < $digit_1 and $digit_5 > $digit_2) {} # also good
      else { $flag++ }
  if ($digit_5 != $digit_4 / 2) { $flag++ }
}

sub check_duplicates {
  # There are no duplicates.
  # Problems with this sub...
  my $candidate = shift;
  my @digits = split //,$candidate;
  foreach my $digit (@digits) {
    #shift(@digits);
    foreach my $check_digit (@digits) {
      if ($digit == $check_digit) { $flag++ }
    }
  }
}

sub check_digit_1 {
  # Digit 1 is 1 less than digit 3.
  # Digit 1 is higher than the sum of digits 4 and 5.
  my $candidate = shift;
  my @digits = split //,$candidate;
  my $sum_4_5 = $digits[3] + $digits[4];
  if ($digits[0] != $digits[2] - 1 or $digits[0] <= $sum_4_5) { $flag++ }
}