Drupada welcomes his guests and is pleased to see that while they were covered with just deerskin, they walked like lions, were well built, tall and with wide shoulders like bulls. They even took the grandeur of the palace in their stride and occupied their seats giving due importance to hierarchy. After a feast fit for kings, chose to occupy the area which was full of implements of war. This further pleased the king.
After treating them with reverence due to brahmins. He said 'Oh illustrious men! Please let us know who you are? Are you khsatriyas? Brahmins? Vaishyas or sudras? Siddhas from devaloka? We are confused. Be frank and clear our doubts so that we can arrange for the wedding suitably.'
Yudhisthira replies 'Maharaja, please do not be worried. Your daughter like the lotus has moved from one sarovara to the other. We are sons of king Pandu'. Then introduces himself and his brothers and adds 'You are our respected elder and I have spoken the truth.'
Drupada overcome with happiness could not even speak and wanted to know all about their escape from the fire. Having heard the story is very upset with Dhritarastra; consoles and promises Pandavas his help in recovering their kingdom. He then suggests 'Let Arjuna now get married on a good day!' Dharmaraja replies; 'Maharaja even I have to be married!' Drupada says, 'In that case you or whoever you choose could marry.'
Yudhisthara comes up with this proposal; 'Maharaja let Draupadi become a queen for all of us. We have always shared and we are not keen to change this now! This is also my mother's wish. So let Krishne marry each one of us with agni as sakshi and become our dharmapatni.' Drupada counters with 'Kaunteya! We know a man has many wives, but have not heard of many husbands! How could such thoughts come to a man of dharma like you?'. Dharmaraja holds firm; 'Maharaja, dhrama is very intricate and we cannot really understand it fully. Anyway we feel it is right and my mother approves. Please to not hesitate or worry.'
Mother Kunthi and Drishtadyumna also join the discussions but the Pandavas do not yield. Finally Drupada agrees 'It seems to be destiny and who can change it?'
As I am reading three versions, narration does get tricky and raises many questions!
For instance Samhita tells us that Draupadi stopped Karna from competing; 'Wait. I will not wed a charioteer's low caste son and bring down my honour as a princess.' Karna returns to his seat humiliated. (Why did his friends keep quiet? May be they were relieved as Karna had the skills and the best chance of a win!)
And it is sage Vyasa who clears the way for the Pandavas to marry Draupadi. Vyasa apears and says that in her last life, she did tapasya for a husband having lost one and mutters five times 'I want a husband.' Lord shiva appears and grants her a boon. 'Since you have said five times, I want a husband, you shall have five husbands in your next birth.' and vanishes into thin air. (All she asked was a for a husband and probably in that life! Not sure that this had something to do with a widow wanting to marry!)
Kamala's version is similar about Vyasa appearing and clearing the way for the marriage. However he does not explain why she was granted a boon for five husbands. And in case of Karna, he misses the fish (the target) by a hair's breadth!