The Pharmacy Scale

Mar 01, 2022

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?



The answer is he takes one pill from the first bottle, two pills from the second bottle, three pills from the third, four pills from the fourth. And if you add it up one plus two plus three plus four or five, you'll have 55 pills that are supposed to be 5 grams each, so it should weigh 275 grams.

And what if it weighed like 276? Then you know, there's just one overweight pill and it came from what bottle? Bottle number one or curtain number one or door number one.

If it weighed 278, you'd know you'd have three overweight pills. And they came from what? Bottle number 7 or whatever!

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