So here’s the new Micro Softy. This one’s about drugs. We’ll talk about last week’s “Bermuda Triangle” puzzle shortly.

The problem: You are a drug enforcement officer who has been told one of the 10 bottles pictured below contains pills laced with a deadly dose of fentanyl. Each bottle contains 800 pills. Each of the fentanyl-laced pills weighs 1.1 grams. The safe pills each weigh 1 gram. Otherwise, the deadly pills and the safe ones look and feel identical.

You have at your disposal an expensive, high-tech scale that measures weights precisely to the nearest milligram (a thousandth of a gram), for a range of 1 to ten billion milligrams. But the demand for time on the scale is high. So every time the scale is used, it costs $5000. Your department works on a tight budget so the scale is to be used as few times as possible.

Here’s the question.  What is the minimum number of weighings required to identify the bottle with the deadly pills?

We’ll give the answer next Monday.

Solution to Micro Softy 19:  The “Bermuda Triangle“

Last week’s problem offered a mysterious triangle where, when sections were rearranged, a hole opened up that wasn’t there before. Look again at the triangle again at the top of the figure below. It has a height of five units and a width of 14 units. When the sections of the triangle are rearranged, as shown at the bottom of the figure, the dimensions remain the same — still a height of five units and a width of 14 units. What’s going on?

The answer is that this triangle is not, in truth, a triangle. The top diagonal line is not a straight line. A small section is shown, blown up at right, where the two triangles meet on the top figure. The dashed line from the blue triangle component, when continued, is the dashed line shown. It lies slightly above the line defined by the yellow triangle component. The sliver of area between the dashed line and the top of the yellow triangle is enough to account for the extra area shown in the bottom triangle when the component triangles are switched.

Here’s another explanation: The blue triangle has dimensions 3 × 8, giving the top line of the blue triangle a slope of 3/8 = 0.375. The yellow triangle is 2 by 5 and the slope of its top line is 2/5 = 0.400. In order to be a straight line where the triangles meet, the slopes must be the same. They are close, but not close enough.

Here are the puzzles (and solutions) from the last eight 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.

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 bags of marbles. 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.

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!