# The Counterfeit Quarters

I’m having trouble understanding the answer. I don’t follow the “Let’s say the genuine coins weigh 10 grams each.” Suppose they weighed 15.5 grams each, then a pile of 10 should weigh 155 grams, but you don’t know that because you didn’t know what each genuine coin weighed.

I don’t think it is a valid puzzle unless they state the weight of a genuine coin in the puzzle question.

Searching the web I saw that when similar questions were asked they gave you the weight of a genuine coin as part of the the question.

Did I miss something?

The problem can NOT be solved as stated,
Either:

1. the weight of a good coin MUST be given OR
2. it must be stated that the coins have integer weight (no fractional parts of a gram.

As proof, I offer “10 and 11/55 grams” as the weight of a good coin and you place the 10 bad coins (either “9 and 11/55 grams” OR “11 and 11/55 grams” in ANY stack) . Note: You may substitute a 1 for the 11 and still get surprising results.

A SIMPLE example will suffice:
Assume that pile #1 is the bad stack and the bad coins are light (i.e. 9 and 11/55 grams"
You will have 1 coin of 9 and 11/55 grams , for 9 and 11/55 grams
and 54 coins of 10 and 11/55 grams ,for 540 and 594/55 grams
A total of 549 and 605/55 grams
which equals …560 grams.
Because it is 10 more than the expected weight you will assume that stack #10 contained HEAVY coins when it was stack #1 which contained LIGHT COINS.

Contact me to know where to send my prize.
P.S. I sent in this same answer in response to the original problem on the first day but I guess there was ‘some sort of problem’ when checked.

You’re right, they left out the weight of the good coin.

That or say that good coins weigh an exact number of grams. (no fractional parts of a gram)

I don’t see how that helps. Both the good and bad coins would then weigh an exact number of grams.

Thanks for confirming my suspicion guys. I wonder what the “winner” gave as an answer. It would be really great to see the producers of Car Talk offer a polite comment about that Puzzler being off base, but people being people I don’t expect that from them.

Call the waaaaaambulance. That’s why it’s called a “puzzler.” Making reasonable assumptions is part of the process. That a worker at the mint knows the weight of a good coin is obvious.

Well, I sure did miss that point. A guy in anti-counterfeiting would most certainly know the weight of a gen-u-wine quarter. Congrats and thanks for wising me up. I’ll be back when my face isn’t so red anymore.

Not sure how it is stated here on the web site, but on the show Ray gave a weight to the good coin (I think he said 10 grams) and the bad coin was either 1 gram more or one gram less. You don’t need to know whether it is less or more, just that it is 1 gram different.

Ray said it can be solved in one weighing of 55 coins. Which is true if you know the two weights in advance…

But I think it can be solved by a single weighing containing less than 55 coins too.

You win! We should have stated in the online version that the person doing the weighing knows how much a real quarter weighs. Sorry about that - we plan to reprimand the junior web lackey if she ever wakes up from her afternoon nap.

Trish Anderton
Car Talk

Thanks for admitting that Trish. As the OP of this discussion I’m pleased that I wasn’t off base with my comment.

I don’t know about the puzzle. But, a few years ago, a distant cousin in my small mountain village asked me to check his late father’s old silver dollars. He had a digital scale, and I searched for their weight.

Then, I grabbed the Bugs Bunny my wife had stuck to the refrigerator. Every dollar he had stuck to the magnet, thus was false.

And, when we weighed them they were not at all the correct weight.