Petting his pet Boston terrier Puddles, eccentric culinary billionaire Sir Irving Spoon stared out the south window of his palatial estate in Yellowstone, Montana. He saw green meadows and, in the distance, snowcapped mountains. He realized that the southern views from his six mansions in various places all had stunning views. He liked that. He summoned his Chief of Staff, Dustin Dubree:

“Dustin, I want a plan to build a small cottage for me somewhere. The one-room house should be roughly square and have four large single-pane picture windows. And each window must have a southern view. You are to use no mirrors, flat screen displays, holograms or other trickery. I want to see what is actually happening outside each of the four windows. As you know, I love southern views!”

Dustin, who was paid a handsome salary for his ingenuity, knew he would be fired if he didn’t come up with an answer. So he thought and thought — and at last he came up with a solution…  

What do you think it was? And now…

Solution to Micro Softy 34: Two Poles and a Wire

Last week’s Micro Softy deals with the electric power grid. It’s a sneaky question.

Two 50-foot telephone poles are connected by a 100-foot power line. How far apart must the poles be to ensure the line doesn’t touch the ground?

Image Credit: mario beauregard - Adobe Stock

Engineering students can use the calculus of variations to show that the line between two poles follows a catenary shape, defined by a hyperbolic cosine. But you don’t need to know this to solve the Micro Softy.

The line is 100 feet long and the poles are 50 feet high. If the poles are touching each other, the line will drop straight down from the first pole, just touch the ground, and then go up 50 feet to the top of the second pole. That’s 100 feet in all.

So if there is any separation in the poles at all, an unbroken power line will not touch the ground.

(The Micro Softy is a weekly feature of Mind Matters News. Links to all the previous ones are available through this one.)

Here are links to all the earlier Micro Softies

Monday Micro Softy 34: Two poles and a wire. Given the measurements, how far apart must the poles be to make sure the power line does not touch the ground? For a solution to last week’s Micro Softy, look at the last week of the previous year.

Monday Micro Softy 33: How fast can a person age? Can a person go from being five this year to being seven next year? The solution to Micro Softy 32 is to remember what types of functions derivatives apply to.

Image Credit: Resni AI - Adobe Stock

Monday Micro Softy 32: Elementary calculus is inconsistent! This is a fascinating puzzle — one that usually stumps even my best graduate students. The solution to Micro Softy 31 is to work back from the end of the alphabet. You will notice a term you can easily solve.

Monday Micro Softy 31: Elementary algebra. How much can an equation be simplified? In last week’s puzzle, the car was handling like a cement mixer because something was wrong with the tires. The solution lies in finding out what that is.

Monday Micro Softy 30: Driving a cement mixer. Why did the car with leaky tires suddenly start handling like a cement mixer, and then, just as suddenly, handle normally again? Micro Softy 29 shows that unambiguous facts can be stated in confusing language but cold hard logic can solve the puzzle.

Links to all the previous Monday Micro Softies

Monday Micro Softy 29: A funeral lament in four lines. The funeral director was puzzled by Dan’s description of his relationship to the deceased but there was no question that his grief was sincere Here, you will also find links to Microsofties 22 through 29 as well.

Monday Micro Softy 21: Finding More of the Deadly Fentanyl Pills. There, you will also find links to Microsofties 11 through 20 as well.

At Monday Micro Softy 11: What Happened to That Other Dollar?, you will find links to the first ten Micro Softies. Have fun!