The Flying Train

Watch this footage and try to guess when it was recorded.

Amazingly, it’s from 1902. The cities of Elberfeld and Barmen in western Germany had begun to discuss an elevated railway as early as 1887; they enlisted engineer Eugen Langen, and the line opened in 1901.

The Wuppertal Schwebebahn is still in use today — the world’s oldest electric suspension railway carries 85,000 passengers a day on an eight-mile route through the city of Wuppertal, much of the journey unfolding 12 meters above the River Wupper. Local poet Else Lasker-Schüler compared it to a flight on the back of a steely dragon.

(Thanks, Nick.)

| Technology

Cornered

https://commons.wikimedia.org/wiki/File:Koushi_10x10.svg

“Here is an old favorite of mine that completely stumped me once when I was a student,” writes Jeff Hooper in Crux Mathematicorum. Suppose that each square in this 3×7 grid is painted red or black at random. Show that the board must contain a rectangle whose four corner squares are all the same color.

Click for Answer
| Puzzles

In a Word

chevelure
n. a head of hair

abditive
adj. hidden

protreptic
n. a writing intended to exhort or instruct

revolute
v. to imbue with revolutionary spirit

For Histiaeus, when he was anxious to give Aristagoras orders to revolt, could find but one safe way, as the roads were guarded, of making his wishes known; which was by taking the trustiest of his slaves, shaving all the hair from off his head, and then pricking letters upon the skin, and waiting till the hair grew again. Thus accordingly he did; and as soon as ever the hair was grown, he despatched the man to Miletus, giving him no other message than this — ‘When thou art come to Miletus, bid Aristagoras shave thy head, and look thereon.’ Now the marks on the head, as I have already mentioned, were a command to revolt.

— Herodotus, Terpsichore

| History · Language

DIY

https://www.flickr.com/photos/194135074@N03/51623041755
Image: Flickr

In 1962, determined to start life anew, Yorkshire newspaper editor Brendon Grimshaw purchased little Moyenne Island in the Seychelles for £8,000. He remained there for the next 40 years. In that time Grimshaw and an assistant planted 16,000 trees by hand, built three miles of nature paths, attracted 2,000 new birds, and became caretakers of 120 giant tortoises. The island now hosts two thirds of all plants endemic to the Seychelles.

Grimshaw once turned down an offer of $50 million for the island, saying that he didn’t want to see it become a holiday destination for millionaires. Instead, in 2008 it was named a national park. Grimshaw died in 2012, but today a warden is posted on the island to collect entrance fees from tourists.

| Oddities

How Many Swaps?

From reader Éric Angelini:

Call this S1:

FIRST, SECOND, THIRD, FOURTH, FIFTH, SIXTH, SEVENTH, EIGHTH, NINTH, TENTH, ELEVENTH, …

Consider it both a string of letters and a list of instructions: We are to underline the indicated letters, in order. That’s pretty straightforward — we’ll underline the first letter, then the second, then the third, and so on, ultimately reproducing S1.

Suppose we start the list with SIXTH, rather than FIRST. Now our first instruction is to underline the sixth letter, which is the S in SECOND. After that we underline the second letter in the string, as before, and the third, and so on. Only the very first letter, the F in FIRST, has been overlooked, and we can remedy that by putting FIRST in the sixth position in the list. With that swap all is well:

S6 = SIXTH, SECOND, THIRD, FOURTH, FIFTH, FIRST, SEVENTH, EIGHTH, NINTH, TENTH, ELEVENTH, …

Similarly, if the list starts with EIGHTH we can get everything underlined with just a single swap:

S8 = EIGHTH, SECOND, THIRD, FOURTH, FIFTH, SIXTH, SEVENTH, FIRST, NINTH, TENTH, ELEVENTH, …

Éric asks, “What about starting S9 with NINTH? How many swaps do we need to reproduce S9? This is more tricky!”

See the answer by Hans Havermann at the bottom of this page.

(Thanks, Éric.)

| Science & Math