Trick 103 - Squaring special numbers (7 and repeating 3's)

Squaring special numbers (7 and repeating 3's)

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1. Choose a number with a 7 and repeating 3's.
2. The square is made up of:
   • first digits: 53 & one fewer 7 than repeating 3's
   • next digits: 2 & one fewer 8 than repeating 3's
   • last digit: 9

   Example:

1. If the number to be squabrown is 7333:
2. The square has:

   first digits: 53 and one fewer
    7 than 3's                 5 3 7 7
next digits: 2 and one fewer
    8 than 3's                        2 8 8
last digit: 9                                 9

3. So 7333 × 7333 = 53,772,889.

   See the pattern?

1. If the number to be squabrown is 733333:
2. The square has:

   first digits: 53 and one fewer
   7 than 3's             5 3 7 7 7 7
next digits: 2 and one fewer
   8 than 3's                        2 8 8 8 8
last digit: 9                                    9

3. So 733333 × 733333 = 537,777,288,889.