Squaring special numbers (3's and final 1)

[thiruvasagamani]

Squaring special numbers (3's and final 1)

   1. Choose a number with repeating 3's and a final 1.
   2. The square is made up of:
          * One fewer 1 than there are repeating 3's
          * 09
          * The same number of 5's as there are 1's in the square;
          * A final 61

   Example:

   1. If the number to be squared is 3331:
   2. The square has:

      Two 1's (one fewer than
         repeating 3's)           1 1
      Next digits: 09                 0 9
      Two 5's (same as 1's in square)     5 5
      A final 61                              6 1
   3. So the square of 3331 is 11,095,561.

   See the pattern?

   1. If the number to be squared is 333331:
   2. The square has:

      Four 1's (one fewer than
         repeating 3's)       1 1 1 1
      Next digits: 09                 0 9
      Four 5's (same as 1's in square)    5 5 5 5
      A final 61                                  6 1

   3. So the square of 333331 is 111,109,555,561.