Pattern excerpts from Mathematical Recreations booksFrom “Mathematical Recreations & Essays”
by W.W.Rouse Ball & H.S.M. Coxeter, Twelfth Ed. p. 13,14.
Find all numbers which are integral multiples of their reversals.
Answer (Sloane's A031877) : for instance, among numbers of four digits,
8712 = 4 x 2178
9801 = 9 x 1089
Numbers that are integer multiples of their reversals are called palintiples.
Dan Hoey made a study and published his Solution to the /arithmetic/digits/palintiples problem.
From “Mathematical Magic Show” by Martin Gardner, page 211
Larger numbers can also be fabricated by repeating each fourdigit number:
From “Figuring - The Joy of Numbers” by Shakuntala Devi, page 70 and 122
Note that 33 equals 1! + 2! + 3! + 4!
"The number 1089 has some peculiar traits.
The following comes from Shakuntala Devi's book
12345679 x 9 = 111111111
Multiplying by 999999999 itself gives a number which is a mirror image of itself
111111111 2 = 12345678987654321
Many people find the above square quite useless but nevertheless fascinating !
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