# What is the smallest number of weighings needed to determine which of the stacks is counterfeit?

There are 10 stacks of coins, each consisting of 10 silver dollars. One entire stack is counterfeit. but you do not know which one. You do know the weight of a genuine silver dollar, and you are also told that each counterfeit coin weighs 1 gram more or less than a genuine coin. You have a pointer scale which you use to Weigh the coins.

What is the smallest number of weighings needed to determine which of the stacks is counterfeit?

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Answer: Only one (1) weighing.

You did not ask how the sampling is done?

If you are taking any Chemistry subjects, you will be able to comprehend the solution.

Anyway here it is:

Procedure:

1) Make sure that you have a scale (analytical balance is recommended) with a capacity to weigh 55 coins plus a container and accurate enough to give a reading to the nearest 1.0000 gram.

2) Label the stacks from 1 to 10. Get one coin from the 1st stack, 2 coins from the 2nd stack, 3 coins from the 3rd stack, 4 coins from the 4th stack, 5 coins from the 5th stack, 6 coins from the 6th stack, 7 coins from the 7th stack, 8 coins from the 8th stack, 9 coins from the 9th stack, and 10 coins from the 10th stack.

6) Get a container large enough to hold the 55 coins and place it on the pan of the scale or analytical balance.

7) Obtain the tare weight. (or Adjust the scale reading to Zero.)

Place all the 55 coins in the container.

9) Obtain the Net Weight. (or Record the weight.)

10) Given: Weight of the genuine silver dollar (for purposes of computation, let this weight be 100 grams).

11) Therefore the total weight of the genuine silver dollar should be 5500 grams.

12) Subtract 5500 from step nine.

13) The difference will be the stack number which contains the counterfeit coins.

Please email me if you disagree with my solution.

Good luck.

1…

take 1 coin from stack 1

2 from stack 2

3 from stack 3

etc… weigh the whole group… and subtract from the expected answer and you have the # of the stack which had the counterfeit

masked man, please delete your response.

i have kids that read this that know right from wrong.

With ten objects (stacks of coins), it should only take a maximum of 3 weighings, or possibly only two.

For instance:

Number the stacks 1-10.

Weigh 1: Compare stacks 1-5 together to stacks 6-10 together.

Whichever group of 5 is lightest and is eliminated.

Assume the stacks 1-5 are heaviest..

Weigh 2: Compare stacks 1-2 together to stacks 3-4 together.

If they are equal, then stack 5 is the counterfeit stack and you have determined it in two comparative weighs.

If they are not equal, eliminate the lighter stacks (assume 3-4).

Weigh 3: Compare stack 1 to stack 2.

The heavier is the counterfeit, and it took 3 weighs.