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Nine nickels and a traditional balance are sitting in front

of you. All nickels have...
Nine nickels and a traditional balance are sitting in front of you. All nickels have the same weight except for one counterfeit, which is slightly heavier than the others. What is the lowest maximum number of times you expect to use the balance to guarantee you've found the counterfeit nickel? Please explain the process you would take.
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7/22/2010
Chris Miller
Chris Miller, Internet Researcher
Category: General
Satisfied Customers: 2,788
Experience: Master's degree in social work, computer knowledge, strong math and science background
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Hello,

 

It actually can be done in just two weighings.

 

(1) Divide the coins into three groups (A, B, and C) of three coins each.
Weigh A against B. If neither group is heavier, rename group C "D"; if A or B is heavier, rename that group "D"
Go to the next weighing.
(2) Weigh two coins from group D against each other. If either is heavier, that one is the counterfeit; if they weigh the same, then it is the third coin in group D that is the counterfeit.

 

Hope this helps!

Chris Miller
Chris Miller, Internet Researcher
Category: General
Satisfied Customers: 2,788
Experience: Master's degree in social work, computer knowledge, strong math and science background
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