Podcast Episode 221: The Mystery Man of Essex County

https://commons.wikimedia.org/wiki/File:Debosnys-Self-Portrait.png

In 1882, a mysterious man using a false name married and murdered a well-to-do widow in Essex County, New York. While awaiting the gallows he composed poems, an autobiography, and six enigmatic cryptograms that have never been solved. In this week’s episode of the Futility Closet podcast we’ll examine the strange case of Henry Debosny, whose true identity remains a mystery.

We’ll also consider children’s food choices and puzzle over a surprising footrace.

Intro:

In 1972 two Canadian scientists set out to figure the number of monsters in Loch Ness.

Winston Churchill’s country home must always maintain a marmalade cat named Jock.

Sources for our feature on Henry Debosnys:

Cheri L. Farnsworth, Adirondack Enigma, 2010.

Craig P. Bauer, Unsolved!, 2017.

George Levi Brown, Pleasant Valley: A History of Elizabethtown, Essex County, New York, 1905.

Caroline Halstead Barton Royce, Bessboro: A History of Westport, Essex Co., N.Y., 1902.

“Debosnys Ciphers,” The Cipher Foundation (accessed Oct. 7, 2018).

Craig P. Bauer, “When Killers Leave Ciphers,” history.com, Nov. 14, 2017.

Nick Pelling, “Henry Debosnys and the Cimbria … ?” Cipher Mysteries, Nov. 16, 2015.

Nick Pelling, “Thoughts on the Debosnys Ciphers …” Cipher Mysteries, Nov. 7, 2015.

Nick Pelling, “The Person Not on the S.S.Cimbria …” Cipher Mysteries, Nov. 17, 2015.

“Guilty of Wife Murder,” [Washington D.C.] National Republican, March 8, 1883.

“Hangman’s Day,” [Wilmington, Del.] Daily Republican, April 28, 1883.

“A Murderer’s Story,” Burlington [Vt.] Weekly Free Press, Nov. 24, 1882.

“A Wife’s Fearful Death,” New York Times, Aug. 6, 1882.

“A Remarkable Man Hanged,” New York Times, April 28, 1883.

The Troy Times of Nov. 23, 1882, had noted, “The prisoner spends his time writing verses, or what he thinks is poetry, and he has over a ream of foolscap paper closely written. Much of this doggerel is written in Latin, French, and an unknown cipher, which Debosnys says is used in Europe quite extensively.” These six cryptograms came to light in 1957 — none has been solved:

Listener mail:

August Skalweit, Die Deutsche Kriegsernährungswirtschaft, 1927.

Emma Beckett, “Food Fraud Affects Many Supermarket Staples, So How Do You Choose the Good Stuff?” ABC, Sept. 3, 2018.

Stephen Strauss, “Clara M. Davis and the Wisdom of Letting Children Choose Their Own Diets,” Canadian Medical Association Journal 175:10 (Nov. 7, 2006), 1199–1201.

Benjamin Scheindlin, “‘Take One More Bite for Me’: Clara Davis and the Feeding of Young Children,” Gastronomica 5:1 (Winter 2005), 65-69.

Clara M. Davis, “Results of the Self-Selection of Diets by Young Children,” Canadian Medical Association Journal 41:3 (September 1939), 257.

This week’s lateral thinking puzzle was inspired by an item on the podcast No Such Thing as a Fish. Here are two corroborating links (warning — these spoil the puzzle).

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 https://futilitycloset.libsyn.com/rss.

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

If you have any questions or comments you can reach us at podcast@futilitycloset.com. Thanks for listening!

Cache and Carry

USC mathematician Solomon W. Golomb offered this problem in the Pi Mu Epsilon Journal, Fall 1971 (page 241):

Ted: I have two numbers x and y, where x + y = z. The sum of the digits of x is 43 and the sum of the digits of y is 68. Can you tell me the sum of the digits of z?

Fred: I need more information. When you added x and y how many times did you have to carry?

Ted: Let’s see. … It was five times.

Fred: Then the sum of the digits of z is 66.

Ted: That’s right! How did you know?

Click for Answer

Common Sense

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A quickie from Raymond Smullyan: On the Island of Knights and Knaves, knights always tell the truth and knaves always lie. Every inhabitant is either a knight or a knave. One day a visiting anthropologist comes across a native and recalls that his name is either Paul or Saul, but he can’t remember which. He asks him his name, and the native replies “Saul.”

From this we can’t know whether the native is a knight or a knave, but we can tell with high probability. How?

Click for Answer

The Red Ball

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An urn contains k black balls and one red ball. Peter and Paula are going to take turns drawing balls from the urn (without replacement), and whoever draws the red ball wins. Peter offers Paula the option to draw first. Should she take it? There seem to be arguments either way. If she draws first she might get the red ball straightaway, and it seems a shame to give up that opportunity. On the other hand, if she doesn’t succeed immediately then she’s only increased Peter’s chances of drawing the red ball himself. What should she do?

Click for Answer

Line Limit

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You own a goat and a meadow. The meadow is in the shape of an equilateral triangle each side of which is 100 meters long. The goat is tied to a post at one corner of the meadow. How long should you make the tether in order to give the goat access to exactly half the meadow?

Click for Answer

Black and White

https://books.google.com/books?id=JTEVAAAAYAAJ&pg=PA96

I just ran across this in Benjamin Glover Laws’ The Two-Move Chess Problem, from 1890. It’s by G. Chocholous. White is to mate in two moves.

Click for Answer

Cube Route

Created by Franz Armbruster in 1967, “Instant Insanity” was the Rubik’s Cube of its day, a simple configuration task with a dismaying number of combinations. You’re given four cubes whose faces are colored red, blue, green, and yellow:

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Image: Wikimedia Commons

The task is to arrange them into a stack so that each of the four colors appears on each side of the stack. This is difficult to achieve by trial and error, as the cubes can be arranged in 41,472 ways, and only 8 of these give a valid solution.

One approach is to use graph theory — draw points of the four face colors and connect them to show which pairs of colors fall on opposite faces of each cube:

https://commons.wikimedia.org/wiki/File:Instant_sanity_graph.png
Image: Wikimedia Commons

Then, using certain criteria (explained here), we can derive two directed subgraphs that describe the solution:

https://commons.wikimedia.org/wiki/File:Instant_insanity_final.png
Image: Wikimedia Commons

The first graph shows which colors appear on the front and back of each cube, the second which colors appear on the left and right. Each arrow represents one of the four cubes and the position of each of the two colors it indicates. So, for example, the black arrow at the top of the first graph indicates that the first cube will have yellow on the front face and blue on the rear.

This solution isn’t unique, of course — once you’ve compiled a winning stack you can rotate it or rearrange the order of the cubes without affecting its validity. B.L. Schwartz gives an alternative method, through inspection of a table, as well as tips for solving by trial and error using physical cubes, in “An Improved Solution to ‘Instant Insanity,'” Mathematics Magazine 43:1 (January 1970), 20-23.

Self-Study

For a puzzlers’ party in 1993, University of Wisconsin mathematician Jim Propp devised a “self-referential aptitude test,” a multiple-choice test in which each question except the last refers to the test itself:

1. The first question whose answer is B is question

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

2. The only two consecutive questions with identical answers are questions

(A) 6 and 7
(B) 7 and 8
(C) 8 and 9
(D) 9 and 10
(E) 10 and 11

3. The number of questions with the answer E is

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

The full 20-question test is here, the solution is here, and an interesting collection of solving routes is here.

(Jim Propp, “Self-Referential Aptitude Test,” Math Horizons 12:3 [February 2005], 35.)