Relationship Numbers Riddle

Replace the question mark with the correct number, given the pair of numbers exhibits a similar relationship?

? : 3839 :: 11 : 1209




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There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
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A man is sitting in a pub feeling rather poor. He sees that the man next to him is extremely rich. He turns to the rich man and says to him, 'I have an amazing talent; I know almost every song that has ever existed.'
The rich man laughs.
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The rich man laughs again and says, 'OK, how about my daughter's name, Joanna Armstrong-Miller?'
The rich man goes home poor. The poor man goes home rich.

What song did he sing? A man is sitting in a pub feeling rather poor. He sees the man next to him pull a wad of £50 notes out of his wallet. He turns to the rich man and says to him, 'I have an amazing talent; I know almost every song that has ever existed.' The rich man laughs. The poor man says, 'I am willing to bet you all the money you have in your wallet that I can sing a genuine song with a lady's name of your choice in it.' The rich man laughs again and says, 'OK, how about my daughter's name, Joanna Armstrong-Miller?' The rich man goes home poor. The poor man goes home rich. What song did he sing?

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There is a cryptic organization called Cicada 3301 that posts challenging puzzles online, possibly to recruit codebreakers and linguists.