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The following poem appeared in the book Imaginary Numbers. It tells how an innkeeper manages to fit 10 guests into 9 rooms, thereby violating what mathematicians call the "pigeon-hole principle."
Ten weary, footsore travelers,
All in a woeful plight,
Sought shelter at a wayside inn
One dark and stormy night.

"Nine rooms, no more," the landlord said,
"Have I to offer you.
To each of eight a single bed,
But the ninth must serve for two."

A din arose. The troubled host
Could only scratch his head,
For of those tired men no two
Would occupy one bed.

The puzzled host was soon at ease –
He was a clever man –
And so to please his guests devised
This most ingenious plan.

In room marked A two men were placed,
The third was lodged in B,
The fourth to C was then assigned,
The fifth retired to D.

In E the sixth he tucked away,
In F the seventh man,
The eighth and ninth in G and H,
And then to A he ran,

Wherein the host, as I have said,
Had laid two travelers by;
Then taking one – the tenth and last –
He lodged him safe in I.

Nine single rooms – a room for each –
Were made to serve for ten;
And this it is that puzzles me
And many wiser men.

Today's challenge: What's the innkeeper's trick?

HINT


(The poem Ten Weary Footsore Travelers appears in the book Imaginary Numbers, edited by William Frucht, and is copyrighted © 1999 by William Frucht. Used by permission of John Wiley & Sons. You may like to view the Amazon.com listing.)

Solution to yesterday's challenge



7 March 2004: Platonic Realms is pleased to announce that we have now made select resources available for download, including The Game of Hex, our humor collection Nowhere Dense, and Mathmo Downloadable Graph Paper. Each is available for a nominal download fee, in association with Amazon.com. Check out all our offerings at the Downloadables Page.

2 February 2004: Congratulations to our principle sponsor, Design Science Inc., on the success of MathType 5 for Windows and Macintosh, and on their outstanding products WebEQ and MathPlayer. MathType is a full-blooded equation editor that lets you create mathematical notation for word processing, Web pages, desktop publishing, presentations, and for TeX, LaTeX, and MathML documents. We at Platonic Realms are very impressed with the new features, especially the outstanding translators for TeX and MathML, and the full support given to preparing display equations for HTML. In fact, MathType 5 for Windows enables you to save an entire Word document as a Web page, with equations that print and display beautifully. By contrast, WebEQ is a complete development environment for putting interactive math on the web, including editing and publishing tools and a Java library for creating point-and-click, interactive math applications within your very own web pages. Finally, the MathPlayer plug-in allows browsers to render MathML encoded equations and notation.
      A SPECIAL NOTE: Design Science Inc., the makers of MathType, have been a supporter of Platonic Realms for most of the seven years we have been online – please show your support for Platonic Realms by visiting their site to learn more.


23 August 2001: If you love quotes, you’ll be pleased to know that the newly redesigned Platonic Realms Interactive Database of Math Quotes is both intuitive and convenient to use. Browse our growing collection of over 300 math-related quotes by author or topic, or search the entire database on a phrase or key-string. We look forward to hearing our visitors’ comments on the new format.

18 July 2001: The PRIME Mathematics Encyclopedia has been completely redesigned and updated to provide quicker, more reliable access and more readable pages. We used many suggestions from our visitors in crafting the new design. Please let us know what you think!

10 April 2001: We've added a whole page of math humor, with jokes, puns, limericks and more from our new e-book collection, Nowhere Dense. The material on the page is rotated daily, and you can also find out more about the book – just visit our new math humor page now!





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