Magic Multiplications with Digits

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
See some patterns generated by arithmetic involving numbers whose digits increase, decrease, or are repeated, or by multiples of some digit. Try to figure out why these curious patterns appear.
Contributed by: Enrique Zeleny (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
A. H. Beiler, Recreations in the Theory of Numbers: The Queen of Mathematics Entertains, New York: Dover Publications, 1964.
Permanent Citation
"Magic Multiplications with Digits"
http://demonstrations.wolfram.com/MagicMultiplicationsWithDigits/
Wolfram Demonstrations Project
Published: March 7 2011