# Josephus Words

By Richards, Dana | Word Ways, August 2011 | Go to article overview

# Josephus Words

Richards, Dana, Word Ways

In the articles on "Magic Spells" (Word Ways, Feb and May 2010) it was proposed that tricks could be performed with a deck of n letter cards. The deck would be prearranged, spelling some word u. There would be a "skip sequence" of integers [k.sub.1], [k.sub.2], ..., [k.sub.n]; the more natural the sequence the better. The magician would spell a new word w = [w.sub.1][w.sub.2][w.sub.3] ... [w.sub.n] as follows: skip [k.sub.1] cards and set the next card aside making it [w.sub.1], skip [k.sub.2] cards and set the next card aside making it [w.sub.2], etc. Each skipped card is returned to the bottom of the deck. Note that the skip sequence defines a permutation [pi] of the the original deck order; w = [pi] (u). We say w is a fixed-point if w = [pi](w). For any given permutation there exists a skip sequence, though it might be hard for a magician to incorporate.

The logological question is to find pairs of words u and w, and a well-motivated skip sequence relating them, that a magician could use with suitable patter. I am not a magician, however, so in this article I will just give pairs of common words. (Pairs using an uncommon word were found but are not reported.)

The story of Josephus Flavius is well-known in recreational mathematics. Forty men stood in a circle and every third man, still standing, was killed. (The puzzle is to find where Josephus should stand to survive to the end.) In our terminology we would say [k.sub.i] = 2 for all i. However [k.sub.1] might be different depending on where you want to start. Let [J.sup.b.sub.a] be the skip sequence where [k.sub.1] = a and [k.sub.i] = b for i > 1. Choosing a = 0 or a = b would be natural in a trick. …

## The rest of this article is only available to active members of Questia

Sign up now for a free, 1-day trial and receive full access to:

• Questia's entire collection
• Automatic bibliography creation
• More helpful research tools like notes, citations, and highlights
• Ad-free environment

Already a member? Log in now.

### Notes for this article

If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

#### Items saved from this article

This article has been saved
Highlights (0)
Some of your highlights are legacy items.
Citations (0)
Some of your citations are legacy items.
Notes (0)
Bookmarks (0)

You have no saved items from this article

Project items include:
• Saved book/article
• Highlights
• Quotes/citations
• Notes
• Bookmarks
Notes
Cite this article

#### Cited article

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Josephus Words
Settings

#### Settings

Typeface
Text size Reset View mode
Search within

Look up

#### Look up a word

• Dictionary
• Thesaurus
Please submit a word or phrase above.
Print this page

#### Print this page

Why can't I print more than one page at a time?

Full screen

## Cited passage

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

## Welcome to the new Questia Reader

The Questia Reader has been updated to provide you with an even better online reading experience.  It is now 100% Responsive, which means you can read our books and articles on any sized device you wish.  All of your favorite tools like notes, highlights, and citations are still here, but the way you select text has been updated to be easier to use, especially on touchscreen devices.  Here's how:

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select.

## Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.

For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

Already a member? Log in now.