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The 4 Puzzle

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Consider the following set of transformations on a given natural number written in base 10:

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1) Put a zero at the end 2) Put a 4 at the end 3) Divide it in half

For instance, by applying the sequence 3313 we can change 4 into 5: 4 -> 2 -> 1 -> 10 -> 5. Given a number up to 100,000, this Demonstration shows the steps to reach it from 4 following these transformations. Can you find a number that needs 53 steps?

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Contributed by: Jaime Rangel-Mondragon (July 2009)
Open content licensed under CC BY-NC-SA

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