Black and White

van dehn chess puzzle

A remarkable thematic chess puzzle by Bodo Van Dehn, 1951. White to move and win.

The solution is 10 moves long, but all Black’s moves are forced. (That’s a very valuable hint.)

Click for Answer

Good Fortune

Letter from Albert Einstein to J.E. Switzer, April 23, 1953:

Dear Sir

Development of Western Science is based on two great achievements; the invention of the formal logical system (in Euclidean geometry) by the Greek philosophers, and the discovery of the possibility to find out causal relationship by systematic experiment (Renaissance). In my opinion one has not to be astonished that the Chinese sages have not made these steps. The astonishing thing is that these discoveries were made at all.

Sincerely yours,

A. Einstein


walkington knight diagonals
Image: William Walkington (CC BY-NC-SA 4.0)

The “Lo Shu square” is the 3 × 3 square enclosed in dashed lines at the center of the diagram above. It’s “magic”: Each row, column, and long diagonal (marked in red) sums to 15. William Walkington has discovered a new magic property — imagine rolling the square into a tube (in either direction), and then bending the tube into a torus. And now imagine hopping from cell to cell around the torus with a “knight’s move” — two cells over and one up. (The extended diagram above helps with visualizing this — follow the blue lines.) It turns out that each such path touches three cells, and these cells always sum to 15. So the square is even more magic than we thought.

More info here. (Thanks, William.)

Podcast Episode 261: The Murder of Lord William Russell
Image: Harvard Digital Collections

In May 1840 London was scandalized by the murder of Lord William Russell, who’d been found in his bed with his throat cut. The evidence seemed to point to an intruder, but suspicion soon fell on Russell’s valet. In this week’s episode of the Futility Closet podcast we’ll follow the investigation and trial, and the late revelation that decided the case.

We’ll also marvel at Ireland’s greenery and puzzle over a foiled kidnapping.


Marshal Ney directed his own execution.

Lewis Carroll invented an alphabet he could write in the dark.

Sources for our feature on the murder of Lord William Russell:

Yseult Bridges, Two Studies in Crime, 1959.

Claire Harman, Murder by the Book: The Crime That Shocked Dickens’s London, 2019.

Thomas Dunphy and Thomas J. Cummins, Remarkable Trials of All Countries, 1870.

J.E. Latton Pickering, Report of the Trial of Courvoisier for the Murder of Lord William Russell, June 1840, 1918.

William Harrison Ainsworth, Jack Sheppard: A Romance, 1839.

“Remarkable Cases of Circumstantial Evidence,” in Norman Wise Sibley, Criminal Appeal and Evidence, 1908.

Samuel Warren, “The Mystery of Murder, and Its Defence,” in Miscellanies, Critical, Imaginative, and Juridical, 1855, 237-271.

“Trial, Confession, and Execution of Courvoisier for the Murder of Lord Wm. Russell: Memoir of F.B. Courvoisier, Lord W. Russell’s Valet [broadside],” 1840.

“Russell, Lord William (1767-1840),” in D.R. Fisher, ed., The History of Parliament: The House of Commons 1820-1832, 2009.

“The Practice of Advocacy: Mr. Charles Phillips, and His Defence of Courvoisier,” Littell’s Living Age 25:313 (May 18, 1850), 289-311.

“English Causes Celebres,” Legal News 14:39 (Sept. 26, 1891), 310-311.

O’Neill Ryan, “The Courvoisier Case,” Washington University Law Review 12:1 (January 1926), 39-46.

Michael Asimow, “When the Lawyer Knows the Client Is Guilty: Legal Ethics, and Popular Culture,” Law Society of Upper Canada 6th Colloquium, University of Toronto Faculty of Law 10 (2006).

J.B. Atlay, “Famous Trials: The Queen Against Courvoisier,” Cornhill Magazine 2:11 (May 1897), 604-616.

Paul Bergman, “Rumpole’s Ethics,” Berkeley Journal of Entertainment and Sports Law 1:2 (April 2012), 117-124.

Abigail Droge, “‘Always Called Jack’: A Brief History of the Transferable Skill,” Victorian Periodicals Review 50:1 (Spring 2017) 39-65, 266.

Albert D. Pionke, “Navigating ‘Those Terrible Meshes of the Law’: Legal Realism in Anthony Trollope’s Orley Farm and The Eustace Diamonds,” ELH: Journal of English Literary History 77:1 (2010), 129-157.

Matthew S. Buckley, “Sensations of Celebrity: Jack Sheppard and the Mass Audience,” Victorian Studies 44:3 (2002), 423-463.

Elizabeth Stearns, “A ‘Darling of the Mob’: The Antidisciplinarity of the Jack Sheppard Texts,” Victorian Literature and Culture 41:3 (2013), 435-461.

Ellen L. O’Brien, “‘Every Man Who Is Hanged Leaves a Poem’: Criminal Poets in Victorian Street Ballads,” Victorian Poetry 39:2 (Summer 2001), 319-342.

Matthew Buckley, “Sensations of Celebrity: Jack Sheppard and the Mass Audience,” Victorian Studies 44:3 (Spring 2002), 423-463.

“This Day’s Examination of the Valet for the Murder of Lord William Russell, M.P.,” 1840, English Crime and Execution Broadsides, Harvard Digital Collections.

Peter Dean, “Death by Servant,” Daily Mail, May 18, 2019, 12.

Robert Douglas-Fairhurst, “The Victorian Melodrama That Led to Murder and Mayhem,” Spectator, Nov. 10, 2018.

Hannah Rosefield, “The Strange Victorian Murder of Lord William Russell,” New Statesman, Oct. 31, 2018.

“Look Death in the Face,” [Liverpool] Daily Post, Sept. 1, 2018, 12.

Alexandra Mullen, “Bloody-Minded Victorians,” Wall Street Journal, July 26, 2013.

Dalya Alberge, “Vital Clue Ignored for 50 Years,” Independent, Dec. 9, 2012.

“Murder of Lord William Russell — Confession of the Murderer,” Sydney Herald, Oct. 20, 1840, 3.

“Murder of Lord William Russell,” New-Orleans Commercial Bulletin, June 16, 1840.

“Further Evidence Concerning the Murder of Lord William Russell,” Spectator, May 23, 1840, 7.

“Francois Benjamin Courvoisier: Killing: Murder,” Proceedings of the Old Bailey, June 15, 1840 (accessed Aug. 4, 2019).

Annalisa Quinn, “Could A Novel Lead Someone To Kill? ‘Murder By The Book’ Explores The Notion,” National Public Radio, March 27, 2019.

Listener mail:

“Local Elections Results,” Irish Times, Aug. 17, 2019.

Wikipedia, “List of Political Parties in the Republic of Ireland,” (accessed Aug. 8, 2019).

Wikipedia, “List of Political Parties in the United States” (accessed Aug. 9, 2019).

Wikipedia, “United States Marijuana Party” (accessed Aug. 9, 2019).

Wikipedia, “United States Congress” (accessed Aug. 8, 2019).

Justin McCurry, “South Korea Mulls Ending Arcane Age System to Match Rest of World,” Guardian, June 2, 2019.

James Griffiths and Yoonjung Seo, “In South Korea, You’re a 1-Year-Old the Day You’re Born. Some Want to Change That,” CNN, June 3, 2019.

Beatrice Christofaro, “In South Korea’s Unique Aging System, Some Babies Turn 2 Years Old the Day After They Were Born. A Bill Is Trying to Change That,” Insider, Jun. 3, 2019.

“Life Term in Murder Contested; Culture Cited on Age,” KDKA Pittsburgh, Aug. 7, 2019.

James Halpin, “Killer Claims Ignorance of Korean Age Custom,” Citizens’ Voice, Aug. 8, 2019.

James Halpin, “Killer Blames Culture Quirk for Age Miscalculation,” Citizens’ Voice, Aug. 7, 2019.

Wikipedia, “National Assembly (South Korea)” (accessed Aug. 11, 2019).

Penelope’s drawing:

penelope's drawing

This week’s lateral thinking puzzle was contributed by listener Ken Murphy.

You can listen using the player above, download this episode directly, or subscribe on Google Podcasts, on Apple Podcasts, or via the RSS feed at

Please consider becoming a patron of Futility Closet — you can choose the amount you want to pledge, and we’ve set up some rewards to help thank you for your support. You can also make a one-time donation on the Support Us page of the Futility Closet website.

Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at Thanks for listening!

Revere’s Obelisk

revere's obelisk

To celebrate the repeal of the Stamp Act, Paul Revere designed an obelisk that was erected on Boston Common on the evening of May 22, 1776. Its four panels, painted on translucent waxed paper borne on a wooden frame, described the phases of the struggle against the act:

1. America in distress apprehending the total loss of Liberty.

2d. She implores the aid of her Patrons.

3d. She endures the Conflict for a short Season.

4. And has her Liberty restord by the Royal hand of George the Third.

At the bottom is the legend “To every Lover of Liberty, this Plate is humbly dedicated, by her true born Sons, in Boston New England.”

It was illuminated by 280 candles, and fireworks and Catherine wheels were launched from its sides. Unfortunately it “took Fire … and was consumed” a few hours a later. This is the only surviving copy of the engraving.

(Thanks, Charlie.)

A Flea’s Journey
Image: Wikimedia Commons

A flea sits on one vertex of a regular tetrahedron. He hops continually from one vertex to another, resting for a minute between hops and choosing vertices without bias. Prove that, counting the first hop, we’d expect him to return to his starting point after four hops.

Click for Answer

“A Rabbit Tamed”

A notable detail from Alexander Morrison Stewart’s Camp, March and Battle-Field (1865): During the Battle of Malvern Hill, a terrified rabbit darted about the battlefield looking for safety until it came upon a Union regiment lying prone:

Ere the rabbit seemed aware, it had jumped into the midst of these men. It could go no farther, but presently nestled down beside a soldier, and tried to hide itself under his arm. As the man spread the skirt of his coat over the trembling fugitive, in order to insure it of all the protection in his power to bestow, he no doubt feelingly remembered how much himself then needed some higher protection, under the shadow of whose arm might be hidden his own defenceless head, from the fast-multiplying missiles of death, scattered in all directions.

It was not long, however, before the regiment was ordered up and forward. From the protection and safety granted, the timid creature had evidently acquired confidence in man — as the boys are wont to say, ‘Had been tamed.’ As the regiment moved forward to the front of the battle, it hopped along, tame, seemingly, as a kitten, close at the feet of the soldier who had bestowed the needed protection. Wherever the regiment afterwards went, during all the remaining part of that bloody day and terrible battle, the rabbit kept close beside its new friend.

“When night came on, and the rage of battle had ceased, it finally, unmolested and quietly, hopped away, in order to find some one of its old and familiar haunts.”

Nose Harmony

English chemist Septimus Piesse likened scents to music:

Odors seem to affect the olfactory nerves in certain definite degrees, as sounds act on the auditory nerves. There is, so to speak, an octave of smells, as there is an octave of tones; some perfumes accord, like the notes of an instrument. Thus almond, vanilla, heliotrope, and clematis, harmonize perfectly, each of them producing almost the same impression in a different degree. On the other hand, we have citron, lemon, orange peel, and verbena, forming a similarly associated octave of odors, in a higher key. The analogy is completed by those odors which we call half-scents, such as the rose, with rose-geranium for its semitone; ‘petit-grain’ and neroli, followed by orange-flower. With the aid of flowers already known, by mixing them in fixed proportions, we can obtain the perfume of almost all flowers.

Using an “odaphone,” or scale, on which harmonies and discords of odors might be studied, his London perfumery Piesse and Lubin produced some of the most important scents of the Victorian era, such as Ambergris (1873), Hungary Water (1873), Kiss Me Quick (1873), The Flower of the Day (1875), White Rose (1875), and Frangipanni (1880).

It had been thought that none of these had survived, but in 2011 two unopened bottles were discovered in the bow of the Mary Celestia, a Civil War blockade runner that had foundered off Bermuda in 1864. The bottles contained Bouquet Opoponax, one of the company’s most popular fragrances, and after analysis with a gas chromatograph, Germany’s Drom Fragrances managed to reproduce the scent in 2014.

“I was shocked at how fresh and floral it was and by the amount of citrus in it,” senior perfumer Jean-Claude Delville told the Star-Ledger. “When the fragrance has been sitting at the bottom of the ocean and aging for so many years you expect something that is oxidized or damaged,” he told CTVNews. “But my first impression was ‘wow’.”

Character Study

Margaret Hamilton on the Wicked Witch of the West:

[There was] a feeling inside that you get. One word: skulduggery. She enjoyed every single minute of whatever she was doing, whether she was screaming or yelling about the fact that Dorothy had those slippers, or sending the monkeys after them all. And the other thing was her utter and complete frustration. She never got what she wanted. She didn’t want Dorothy and she didn’t want any of those other characters. She just wanted those slippers. And today, according to law, she probably would have had them. They were her sister’s, and she would have been in line to inherit them. But she didn’t get there fast enough.

(From Aljean Harmetz, The Making of The Wizard of Oz, 1977.)