Last Monday’s puzzle was titled the Twin Paradox. We’ll answer that one in a bit, but first, here’s this week’s Micro Softy:

The Bermuda Triangle is a region in the North Atlantic Ocean, notorious for the mysterious disappearances of ships and aircraft under unexplained circumstances.

With this in mind, take a look at the triangle at the top of the figure shown below. It has a height of five units and a width of 14. If sections of the triangle are rearranged as shown at the bottom of the figure, the triangle still has the same dimensions.

But look closely. There is more area in the bottom triangle, as shown by the small black rectangle. Yet the other squares are all accounted for. Thus the rearranged triangle on the bottom has more area than the one on top, even though the bottom triangle still has a width of 14 and a height of five.

 This extra area symbolizes the black hole where ships vanish in the real Bermuda Triangle.

What’s going on here? Where did this extra area come from? Look for the answer next Monday!

Solution to Monday Micro Softy 18:  The Twin Paradox   

Last week’s puzzle has a flat forehead solution: if you haven’t solved it, when you hear the answer, you will slap yourself in the forehead with the palm of your hand and say “of course!”

Here’s the riddle again: Curt and Rod look a lot alike. They were born on the same day of the same year and have the same mother. Yet they are not twins. How come?

The answer is that they are two thirds of a set of triplets (flat forehead time!). Their sister, Clarice, keeps the books for Curt and Rod’s drapery business.

Here are the puzzles (and solutions) from the last seven Mondays:

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?

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.

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.

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?

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.

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?

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!