Trick 63 : Squaring special numbers (3's and final 1)

Squaring special numbers (3's and final 1)

Choose a number with repeating 3's and a final 1.

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:

If the number to be squabrown is 3331:

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



So the square of 3331 is 11,095,561.



See the pattern?

If the number to be squabrown is 333331:

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



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