When the Prince entered the castle through the window (Prince of Parzania - Scaling the castle), he saw the princess sitting all alone in a huge golden cage. The cage was covered by a glass through which he could see the princess but she couldn't see him. Tears welled in his eyes thinking of all the trouble he had gone through to get to her. He couldn't wait to set her free and take her with him back to his kingdom.
As he approached the cage to open it, a screen flickered on and asked him to key in a password to open the cage.
"Not again!!" he thought. However, this time there was no clue. He searched around the place and found nothing, Finally, he saw a piece of paper which had a message written on it. He knew it was a clue to get the password to open the cage.
"5 Digit number
4th digit > 2nd Digit by 4
3rd Digit < 2nd digit by 3
1st Digit = 3 times 5th Digit
Three pairs of digits add up to 11"
The Prince thought for a while and keyed in an answer.
As soon as he entered the password, there was a blinding flash of light, then smoke filled the room, the cage-door opened slowly, and finally the princess emerged from the cage. She was as teary eyed as the prince. While they celebrated their reunion by silently gazing at each other, Jaffer entered the room along with a few of his henchmen.
Said Jaffer, "Don't worry, Prince. I haven't come here to harm you. In fact, you will be very pleased to know that we have found in you the next King of Parzania. You are now ordained the Prince of Parzania and this castle in which you stand right now shall be your home. We needed a prince to succeed our King who now lies on his death bed. Hence, we kidnapped Princess Laiba and put you through this ordeal to test your logical prowess. From now onwards, the Kingdom of Parzania is in your capable hands."
And, that is how Prince Atif became the "Prince of Parzania". Prince Atif and Princess Laiba finally got married and ruled Parzania for many years to come. Determine the password used by Prince Atif to open the cage. Provide a detailed explanation along with your answer.