Can you steal the most powerful wand in the wizarding world? - Dan Finkel
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The fabled Mirzakhani wand is the most powerful magical item ever created. And that’s why the evil wizard Moldevort is planning to use it to conquer the world. You and Drumbledrore have finally discovered its hiding place in a cave, but the wand is hidden by a system of 100 magical stones. Can you figure out how to get to the wand before Moldevort? Dan Finkel shows how.
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Is there anything special about the number 100 in this problem? How would the outcome change (or would it) if there were 50 stones instead of 100? What if there were 500 stones? Which parts of the argument hold, and which don’t?
Here’s another argument to attack this problem based on the idea that the number doesn’t really matter. Solve the riddle with only two stones. Then suppose you had solved it with any number of stones, say, N stones. Could you solve it with N + 1 stones? This type of argument is known as induction, and can help us solve some tricky problems, like this one.
Here’s another argument to attack this problem based on the idea that the number doesn’t really matter. Solve the riddle with only two stones. Then suppose you had solved it with any number of stones, say, N stones. Could you solve it with N + 1 stones? This type of argument is known as induction, and can help us solve some tricky problems, like this one.
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