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Palindromic Patterns

Watch the pattern forms when 37 is multiplied by 3 and its multiples :
From “Figuring - The Joy of Numbers” by Shakuntala Devi, page 125.

37 x 3 = 111
37 x 6 = 222
37 x 9 = 333
  37 x 12 = 444 
37 x 15 = 555
37 x 18 = 666
 37 x 21 = 777
37 x 24 = 888
37 x 27 = 999

[ August 10, 2000 ]
Hugo Sánchez from Caracas, Venezuela is fascinated by palindromic patterns.
This plate is too small to display them all, hence I shall show only the most beautiful ones.

 37 x 12 = 444 
37 x 1212 = 44844
37 x 121212 = 4484844
General formula rood 37 x (12n) = 4(48n-1)44  [n⩾1]

37 x 33 = 1221 
37 x 333 = 12321
37 x 3333 = 123321
General formula rood 37 x (3n) = 12(3n-2)21  [n⩾2]

91 x 111 = 10101
91 x 1111 = 101101
91 x 11111 = 1011101
General formula rood 91 x 1(1n) = 101(1n-2)01  [n⩾2]

Other Hugo Sánchez WONplates
won106.htm won153.htm won162.htm


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