A Puzzle Forest

An unusual problem by Reddit user cgibbard, from a discussion in 2010:

Here’s a representation of 101010 for you to figure out.

      *             *      *
      |             |      |
   *  *  *   *  *   *  * * *
   |  |   \ /    \ /    \|/
*  *  *    *      *      *

As a bonus, here’s the corresponding representation for 42:

   * *   *
   |  \ /
*  *   *

The puzzle is to find the rule for this representation.

A commenter wrote, “This puzzle is really clever and very rewarding to figure out.”

Click for Answer

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.)

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

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

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.