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Prologue: A paradox is something that doesn't make sense. For example if I say "I lie", what do I mean? If I am lying, then I am not. But if I'm not, then I am! There are plenty of paradoxes lying around, but here's one of my favourite.
Storylogue: Alex and Wizi were the best of friends. They did everything together, apart from all the things they didn't do together. They were busy playing cards at Alex's house when a spaceship landed outside their house. Alien landings were quite common then --- a couple of mathematicians had visited the previous week. Still, in a feeble attempt to promote intergalactic tourism by showing earthling hospitality, the two kids ran out to meet the visitor.
Two minutes later, they were busy having some Alpha Centauri tea which the trillion-eyed visitor had brought. The talk turned from the latest soccer scores (Mars 10, Earth 9 1/2) to more mundane matters. Eventually Ebdntexdiogjire III (Ebby for short) looked at them through eye no. 5246134 and spoke.
"You know, I'm a researcher at the Plutonion school for Solar System life forms, and I'd like to know if you can help me with an experiment."
The kids agreed. Ebby placed two boxes in front of them, labelled 1 and 2.
"Box 1 contains $1000. Box 2 contains $1 000 000 or nothing. You must take either Box 2 or both. I will try to predict what you will take, and will determine the contents of 2 beforehand. If I think you'll take just box 2, then I'll a million in it. If I think you'll take both boxes, 2 will be empty. Alex, you choose first."
"Let me get this straight."said Alex, "You've made your choice already. So at this moment, Box 2 has a million or nought. Whatever I do won't change that. So I might as well take both boxes! That way I'll get $1000 more than I will be taking just Box 2."
"Apparently so," replied Ebby "But I do warn you --- this experiment has been carried out in over a million cases, and in all but one case I've predicted correctly. That was with a farmer in Hungary."
Alex didn't bother with that. He opened both boxes and found himself just $1000 richer. He was furious.
"Well, if I take just Box 2, then there's a good chance that you predicted that, and I'll become a millionaire!" said Wizi.
Ebby put two new boxes on the table, indicating that he'd made his prediction the previous night. Wizi opened Box 2 only and was screaming with delight when he found he was a thousand times richer than Alex. Alex was no longer furious --- now he was hopping mad.
"I don't believe you made your decision before. I think you somehow removed the million bucks from Box 2 when you saw that I'd taken both boxes. After all, your technology is that advanced." he said.
"You're right," said the alien "I could have done that. But I didn't. Close your eyes Alex. Good. Now here are two more boxes. As Wizi can clearly see, they're transparent. Wizi can see what's in both boxes, though you can't. No peeping! What do you choose?"
"My argument still applies, right? So I'll take both."
Alex opened his eyes and saw that Box 2 was empty. Wizi was looking rather horrified at the alien and asked him how he managed to do that. Ebby smiled and motioned to them to switch places. Wizi again chose Box 2 only, and it was Alex's turn to look horrified.
"You're not human!" he said to Ebby.
"That's pretty obvious." replied the alien as he opened Box 2 and gave a sack of money to Wizi.
They repeated the experiment ten more times. Even when Alex took box 2 only or Wizi took both boxes, Ebby always predicted correctly. Finally Alex took a coin out of his pocket and announced that he was going to use it to make his decision. Heads, one box, tails, two boxes.
"I forgot to mention. Any use of random events like coin tossing is forbidden." Ebby said.
Wizi pocketed his change.
Epilogue: Ebby flew off to Sri Lanka after lunch to visit the house of a well known cricketer. Wizi and Alex invested all their money in the Stock Exchange and were soon back to being broke. Arguments about the paradox, which was invented by a University of California physicist William Newcomb in 1960, still continue.