Prove the following using strong induction. Suppose you are gifted a collection of 3n pokéballs; all of the the pokéballs have the same size and weight except for one which is slightly heavier, and otherwise look and feel exactly the same as the others. You are tasked with identifying the heavy pokéball and have at your disposal a set of balancing scales which can be used to compare the weights of two collections of pokéballs. The scales can show whether the two collections have the same weight, or can show which collection is heavier if the weights are different. Prove using strong induction that you can identify the heavy pokéball out of 3n pokéballs using n weighing operations.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Prove the following using strong induction. Suppose you are gifted a collection of 3n pokéballs; all of the the pokéballs have the same size and weight except for one which is slightly heavier, and otherwise
look and feel exactly the same as the others. You are tasked with identifying the
heavy pokéball and have at your disposal a set of balancing scales which can be used
to compare the weights of two collections of pokéballs. The scales can show whether
the two collections have the same weight, or can show which collection is heavier if the
weights are different. Prove using strong induction that you can identify the heavy
pokéball out of 3n pokéballs using n weighing operations.

 
 
 
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