Pharmacy Puzzler (New and Improved)

It's time for this week's puzzler. Now, do you remember the name of the druggist in last week's puzzles George Bailey?

Well, that was just the setup for this puzzle. We thought we'd try another pharmacist puzzle. So it's exactly the same puzzle, with a little twist.

I'll just state this as if there were no puzzle last week. So here it is. You have a drugstore in which you have all these bottles of pills, our shipment of pills has arrived. There are a couple of 100 pills. 300 pills. 400 pills in each but big bottles.

And in last week's puzzle was, you had one bottle of pills where the pills were faulty. They were overweight. Okay, so you had to figure out, with one weighing on your fancy analytical scale, you had to figure out a clever way to weigh the pills and determine at a glance which bottle was the one with the defective and overweight pill.

And you knew that a good pill weighed five grams in a bad pill, an evil pill, weighed six grams. You were told that there was only one bottle that had faulty pills.

And the solution was to take one pill from the first bottle two pills in the second bottle with three pills with that. Okay, so if you were like six grams overweight, you knew that it was the sixth bottle. Two grams overweight, you know it was the second bottle. A very clever solution.

So now you get the telegram that says you might have, let's say you have six bottles of pills. Could be any number but let's say it's six bottles of pills. And the telegram says there could be any number of bottles that have faulty pills.

So the good bottles have pills that weigh five grams each. But either one or two or three or four or maybe all six bottles have pills in them that weigh six grams. And the entire contents of the bottle would have bought the pill, it wouldn't be just one faulty pill in the bottle, it would be an entire right bottle. And remember they would look like the regular pills.

The question is how can George Bailey or anyone do this with one weighing? Or can it be done?

Can it be done with, one weighing, to determine if any of the bottles have defective pills in them? Because it could be anyone bottle that has defective pills or it could be all six of them?, or none, or anything between. Right? So it's a two-part question. A: Can you do this with one weighing? And part 2: How?

It's time for this week's puzzler. Now, do you remember the name of the druggist in last week's puzzles George Bailey?

Well, that was just the setup for this puzzle. We thought we'd try another pharmacist puzzle. So it's exactly the same puzzle, with a little twist.

I'll just state this as if there were no puzzle last week. So here it is. You have a drugstore in which you have all these bottles of pills, our shipment of pills has arrived. There are a couple of 100 pills. 300 pills. 400 pills in each but big bottles.

And in last week's puzzle was, you had one bottle of pills where the pills were faulty. They were overweight. Okay, so you had to figure out, with one weighing on your fancy analytical scale, you had to figure out a clever way to weigh the pills and determine at a glance which bottle was the one with the defective and overweight pill.

And you knew that a good pill weighed five grams in a bad pill, an evil pill, weighed six grams. You were told that there was only one bottle that had faulty pills.

And the solution was to take one pill from the first bottle two pills in the second bottle with three pills with that. Okay, so if you were like six grams overweight, you knew that it was the sixth bottle. Two grams overweight, you know it was the second bottle. A very clever solution.

So now you get the telegram that says you might have, let's say you have six bottles of pills. Could be any number but let's say it's six bottles of pills. And the telegram says there could be any number of bottles that have faulty pills.

So the good bottles have pills that weigh five grams each. But either one or two or three or four or maybe all six bottles have pills in them that weigh six grams. And the entire contents of the bottle would have bought the pill, it wouldn't be just one faulty pill in the bottle, it would be an entire right bottle. And remember they would look like the regular pills.

The question is how can George Bailey or anyone do this with one weighing? Or can it be done?

Can it be done with, one weighing, to determine if any of the bottles have defective pills in them? Because it could be anyone's bottle that has defective pills or it could be all six of them, or none, or anything between. Right? So it's a two-part question. A: Can you do this with one weighing? And part 2: How?

Answer the Puzzler »

Remember last week's puzzler?

The Pharmacy Scale

Let me launch right into the new puzzler. We've been blessed over the years with puzzles that we have encountered. They've come into our gravitational sphere, so to speak. We've had some great ones. I mean, the Monty Hall puzzle, for example, was a great one. The other one that comes to mind is the one from which My Fair City came.

That was a good one. And how about the three men in the hotel? I mean, that was one of the greats! And I was thinking about these puzzles and how great they are. And I was comparing them to today's lousy puzzle. On that note, here's today's puzzle.

Now, imagine this scene. It's a pharmacy. A grizzled old pharmacist behind the desk.

And he's got a young assistant, named George Bailey. He's received a shipment of pills. And George has dutifully put them on the shelf.

And the next day, I guess he gets in the mail a notification that there's something wrong in one of the bottles of pills he got. All the pills, in fact, are faulty. They are one gram too heavy.

These are, just for clarification purposes, these are all these are 20 bottles of the same medicine. So all the pills are supposed to be identical.

They look all the same. You can't look at any of the pills and say, "Oh, this one's heavier than the other one, being different by one gram only."

And there were only a few pills in every bottle. And another thing, all the bottles have different weights, so you could never put a whole bottle on a scale and say, "Well, this is the heavy one!" Because the bottles might weigh different amounts.

So the grizzled old pharmacist, the mean, old pharmacist assigns this job to sweet old George. He figures out an easy way to do it. In fact, he figures out how to do it with only one weighing on the scale.

So he knows how much a real non-counterfeit pill weighs, but remember, one whole bottle has bogus pills in it, the bottles don't necessarily weigh the same, and the bottles don't have the same number of pills in them.

So how does he do it?