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Problem Statement



There are twelve items numbered 1 through 12. All of the values or "weights" are the same except one item whose value is either greater than or less that the other 11 by an unknown amount.

One can compare the sum of the values of a number of items in a set with the sum of the values of items in a disjoint set to see which one is greater. 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. 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......

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Approximate Word Count: 1531
Approximate Pages: 7 (250 words per double-spaced page)

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