Monday Micro Softy 21: Finding More of the Deadly Fentanyl Pills
The solution to last week's deadly pills puzzle can be found, as we'll see, by numbering the bottles. But this week we make the challenge tougher…This week’s Micro Softy is a more difficult version of last week’s. So let’s reverse the usual order and look at the solution to last week’s puzzle first.
Here’s the problem: As a drug enforcement officer, you are presented with 10 bottles, each containing 800 pills. Among them, one bottle’s pills have been laced with a deadly dose of fentanyl. The regular pills weigh exactly 1 gram but the fentanyl-laced pills weigh 1.1 grams each. They differ only by weight; otherwise, the two types of pills look and feel identical. You have access to a high-tech scale that precisely measures weight. But the scale is expensive to use. Your task is to figure out the minimum number of weighings needed to identify the bottle that contains the fentanyl-laced pills.
Answer: Only one weighing is necessary.
Here’s how:
Number the bottles from #1 to #10. Take one pill from bottle #1, two from bottle #2, three from bottle #3, right up to 10 pills from bottle 10. That’s 55 pills in all. Weigh all the loose pills together. If the weight is 55.1 grams, bottle #1 has the fentanyl pills (because you only took one pill). If 55.2, it’s bottle #2 (because you took two pills). It’s bottle #3 if the weight is 55.3 grams because you took three pills from it. And so forth.
This week’s Micro Softy is much more difficult
The problem is the same as above except for one thing: We don’t know how many bottles contain the fentanyl-laced pills. It could be two bottles, it could be all ten bottles — or no bottles at all. How can we identify all of the bottles containing fentanyl using one single weighing? You can assume 2000 pills.
Here’s a hint: It helps if you know binary numbers. Answer next Monday!
Here are the puzzles (and solutions) for the last nine Mondays:
Monday Micro Softy 12: Can You Connect the Dots? You may use no more than four perfectly straight lines and the lines must be connected. This classic puzzle in simple graph theory resulted in a commonly used phrase. Can you guess it?
Monday Micro Softy 13: Garbage Trucks, String Theory… … and Stained-Glass Windows. What connects them? These puzzles, associated with the great mathematician Leonard Euler (1707‒1783), have a practical use, for example, in laying water pipes.
Monday Micro Softy 14: How Did the Blind Ticket Seller Know? This puzzle doesn’t require math skills so much as advanced common sense reasoning. About last week’s solution, given here: If you code, the second part of the puzzle could also be offered to a computer.
Image Credit: CIGI - Monday Micro Softy 15: What Happens to the Hole in a Hot Washer? When a washer ring is heated, does the hole in the center get bigger or smaller? The answer to last week’s Micro Softy turns on the question of what form of currency Claire gave the blind ticket seller. Did you guess it right?
Monday Microsofty 16: The Leaky Bucket. The puzzler must decide where to place the hole for maximum distance of outward flow. And explain how the problem would change on the Moon. One hint for the solution to the hot washer problem, given here, is the old trick for getting a tight lid off a jar: Running hot water over it.
Monday Micro Softy 17: Mixed-up >a href=”https://mindmatters.ai/2025/03/monday-micro-softy-17-mixed-up-bags-of-marbles/” target=”another”/a< The bags-of-marbles puzzle is comparatively simple: How many marbles must you pull from the mislabeled bags in order to relabel them correctly? There’s a rough solution to the “leaky bucket” problem but an exact solution requires some use of fluid dynamics. But the Moon, surprisingly, changes nothing.
Monday Micro Softy 18: The Twin Paradox. It’s not Einstein’s Twin Paradox but it will certainly set you thinking anyway. About the mixed-up bags of marbles: The key question is, from which bag would drawing a marble give you the most information?
Monday Micro Softy 19: The “Bermuda Triangle” Why does the strange triangle, rearranged, appear to have a bit of extra area? The solution to the Twins Paradox lies in considering the possibility that Curt and Rod were not alone in the womb.
Monday Micro Softy 20: Which Bottle Holds the Deadly Fentanyl? You can find out the answer, using advanced technology — but there is a price. About the “Bermuda Triangle” puzzle: Look closely. Are they both really triangles?
Note: At Monday Micro Softy 11: What Happened to That Other Dollar?, you will also find links to the first ten Micro Softies. Have fun!
