Counterfeit Coins: Newsletter Challenge (01/23/07)

Is that the only solution or is there another way to conclude.

I found a different method

Chuck

Chuck -

As you can see by reading the other answers, there are several different successful methods. They all seem to start by weighing four against four, but after that the methods differ.

If you have another system that isn't listed here, please post it so we can see!

The Last Post

The question does not stipulate that you cannot obtain 12 more none fake coins to balance with the 12 you have, doing this will determine the over or under weight value of the fake.

Then balance 6 against 6 to cut it down to 3 coins on each side and then 1 against 1 to determine the bad one.

Don

Interesting premise! But I don't see how it can work in three weighings. Here's what I think you're saying:

1) Weigh 12 good against 12 unknown (determine light/heavy).

2) Weigh 6 unknown against remaining 6 unknown (narrow it down to 6)

3) Weigh three suspects against remaining three (narrow it down to three)

...to determine which of the final three is bad, you'd need one more weighing.

Am I missing something?

After the second weighing you will have only 3 suspects as they will be either up or down according to the weight determined in the first weighing. Weigh two of these against each other this will show the off weight coin is either up or down on the balance or if they balance the off weight coin is the remaining one.

Don

I don't understand how you get it down to 3... Let's take a scenario. First we mark our original coins with letters, A through L.

1) Weigh original coins A-L against twelve good coins. Let's say the A-L side is heavier, so we know the bad coin is heavy.

2) Weigh A-F against G-L. Let's say the A-F side is heavier, so we know coins G-L are good, but all six of the heavier coins are still suspect, right?

Now, what do I do in step 3?

Re: Last Post & #103

You are Right, I lost count of my weighings!

Don

sexy answer!!