World!Of
Numbers  WON plate
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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 37 x (12n) = 4(48n-1)44  [n>=1]

37 x 33 = 1221
37 x 333 = 12321
37 x 3333 = 123321

General formula 37 x (3n) = 12(3n-2)21  [n>=2]

91 x 111 = 10101
91 x 1111 = 101101
91 x 11111 = 1011101

General formula 91 x 1(1n) = 101(1n-2)01  [n>=2]  Other Hugo Sánchez plates won106.htm won153.htm won162.htm   A000084 Prime Curios! Prime Puzzle  Wikipedia 84 Le Nombre 84 Numberland 84 ```

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