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IMP POW 15: 12 Bags of Gold

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Issue:

Miscellaneous

 

Written by:

Paul D

 

Date added:

December 9, 2016

 

Level:

University

 

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No of pages / words:

5 / 1362

 

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9018 times

 

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This comparison is also called "weighing." Find the least number of ways to determine which item has a greater or lesser value. Process From the previous POW it was concluded that it would take 5 weighings as described by the equation for an unknown item value: However, this is an overestimate as there is a way to determine the lighter of nine items with only two weighings...
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This was overlooked in the last POW (Eight Bags of Gold). Nine items can be weighed by dividing into three sets of size three. Comparing two sets together would determine which set contained the lighter item. With the last weighing, one can determine the lightest item. This raises the limit of weighings meaning that it would take a mere three weighings to single out the different item out of a set of 27...
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