Rob Fathauer discusses the ins and outs of the mathematical toy business, and we ask: For which numbers is the sum of digits the same as the sum of digits of twice the number. For example:

The sum of the digits of 351 is 9 and the sum of the digits of 2 x 351 = 702 is also 9.

1) If a number has this property, can we always rearrange its digits and obtain another number with this property (513, 135, etc all have it)

2) Which powers of 2 have this property?

3) And most of all, can you give a simple characterization of the numbers with this property, in terms of just the digits themselves?

 

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Our favorite new and not-so-new products of 2008!

 

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Check out these great gifts!

• Zome is an incredibly powerful construction system!
• the great puzzles of Puzzellation (available at Barnes and Nobles)
• The terrific puzzle computer game DROD
• The Magic Mirror Image Coloring Book
• The Riddles of the Sphinx by David J Bodycombe, an amazing compendium of puzzles, of hundreds of kinds, at all levels of difficulty, with historical essays to boot!
• Which leads us to Nikoli, the great Japanese puzzle co! (Rules can be found here)
• The Princeton Companion to Mathematics is a landmark classic. A must-have for every serious student, researcher or amateur.
• How Round is Your Circle just one of the many fantastic titles out on Princeton University Press
• AK Peters is another fantastic press, with a wide range of interesting math and CS titles, including, ahem, the Symmetries of Things.
• Binary Arts/ThinkFun is another source of great puzzles!
• And the authors Martin Gardner and Ivan Moscovitch are always fantastic!

Hope this helps and have fun!! Let us know how it works out!

Happy Holidays from the Math Factor!

 

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Now, really, tell me, what good is a podcast if you can’t promote your beautiful new book?

We are very very pleased to announce the publication of The Symmetries of Things, a comprehensive, modern account of the mathematics of symmetry, complete with over 1000 illustrations!

We visit a giant model of a four-dimensional polyhedron, made of the fabulous Zome math construction toy. Paul Hildebrandt, president of Zome, weighs in!

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