Thursday, June 4, 2009

1089 pattern and facts.

* Multiplying the number 1089 by the integers from 1 to 9 produces a pattern: multipliers adding up to 10 give products that are the digit reversals of each other. 

1089 x 1 = 1089
1089 x 2 = 2178 
1089 x 3 = 3267 
1089 x 4 = 4356 
1089 x 5 = 5445  (Palindrome)
1089 x 6 = 6534  (reverse of 4356)  
1089 x 7 = 7623  (reverse of 3267) 
1089 x 8 = 8712  (reverse of 2178) 
1089 x 9 = 9801  (reverse of 1089) 

Also note the patterns within each column. First column is increasing order of 1 to 9, second column is increasing order of 0 to 8, third column is reverse of second column and fourth column is reverse of first column.

* Another cool aspects are
-  1/1089 = 0.00 09 18 27 36 45 54 63 72 81 ..... remember the 9 table
-  1/9801 = 0.00 01 02 03 04 05 06 07 08 09 10 11 12 13 14... 

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