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This one weird trick will get you infinite gold - Dan Finkel

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A few years ago, the king decided your life would be forfeit unless you tripled the gold coins in his treasury. Fortunately, a strange little man appeared and magically performed the feat. Unfortunately, you promised him your first-born child in exchange for his help — and today he’s come to collect. Can you figure out how to outsmart the man and keep your baby? Dan Finkel shows how.

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There are many ways to generalize this situation. Here are a few:

-What would the magic do to 17 coins? To 23? To 30?

-Is it possible to end up with any number of coins after applying the magic once? For example, if I want the bag to hold exactly 47 coins, is there a number I can put in first that will end up with 47 coming out?

-Can you write a formula or description for how the magic behaves?

-What if the bag quadrupled the coins when you applied it three times. Could you find what would happen to 13 coins in this case? Does this situation generalize?

For more on the basics of functions, check out this video from Khan Academy.

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Meet The Creators

  • Educator Daniel Finkel
  • Director Gavin Edwards, Movult
  • Narrator Addison Anderson
  • Music Cem Misirlioglu
  • Sound Designer Cem Misirlioglu
  • Senior Producer Anna Bechtol
  • Producer Sazia Afrin
  • Editorial Director Alex Rosenthal

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