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# Counterfeit Coins

## Question

There are twenty-four half-dollar coins stacked in three identical piles.  Two piles are real and one is counterfeit.  The individual counterfeit coins look exactly like the others but either weigh a gram more or less from the others.  The net weight of each pile is exactly the same.  How many weighs on a balance will it take to determine which pile is false?

How many weighs would it take if there were an equal distribution of false coins in each pile?

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First part

Two weighings
(1) weigh AAA vs BBB
Equal? -> C is counterfeit
Unequal? -> C is good
(2) weigh AAA vs CCC
Equal? - > B is counterfeit
Unequal? -> A is counterfeit

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There are twenty-four half-dollar coins stacked in three identical piles.  Two piles are real and one is counterfeit.  The individual counterfeit coins look exactly like the others but either weigh a gram more or less from the others.  The net weight of each pile is exactly the same.  How many weighs on a balance will it take to determine which pile is false?

How many weighs would it take if there were an equal distribution of false coins in each pile?

Agree with Ed on first part. Can you clarify the second question?

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There are twenty-four half-dollar coins stacked in three identical piles.  Two piles are real and one is counterfeit.  The individual counterfeit coins look exactly like the others but either weigh a gram more or less from the others.  The net weight of each pile is exactly the same.  How many weighs on a balance will it take to determine which pile is false?

How many weighs would it take if there were an equal distribution of false coins in each pile?

Agree with Ed on first part. Can you clarify the second question?

On the first one we had an entire column of false coins.  Now in this situation, each column has precisely 8 false coins.  What is the fewest amount of weighings needed to find all of the false coins?

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On 12/4/2015 at 5:56 AM, BMAD said:

On the first one we had an entire column of false coins.  Now in this situation, each column has precisely 8 false coins.  What is the fewest amount of weighings needed to find all of the false coins?

If each column has precisely 8 false coins and each column is composed of 8 coins, then...

Spoiler

...it would take 0 (zero) weighings, as logic can be used without the scale to know each of the twenty-four coins are false.

..., or, perhaps

On 12/3/2015 at 11:59 AM, BMAD said:

There are twenty-four half-dollar coins stacked in three identical piles....

is intended to be interpreted as each pile has twenty-four coins, for a total of 72 coins in the three piles?

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