Number Devil (I) The First Night

Reading this title, The Number Devil - a Mathematical Adventure, written by Hans Magnus Enzensherger... about a relationship that changes one's perpsective and attitude towards Mathematics.

It started with numbers... the most fundamental element in the numeric system.
How "1" has wonderfully introduced other numbers into to picture!

starting from 1 x 1 = 1
11 x 11 = 121 (where 2 is introduced)
111 x 111 = 12321 (where 3 is introduced)
Well, there are 2 things to observe:

• The introduction of the 'new' number as the "size" of the number is increased (by a certain pattern)
• The repeated pattern within the answer - the number reads the same from left to right or vice versa!

What happens when there are 9 "1"s?

• 111,111,111 x 111,111,111?
• We would get 12345678987654321 (according to the pattern)
• So is it true?

Then what's next? when we have 11 "1"s? Interesting!

Well, the calculator has failed us because it would not be able to display so many figures. How about the spreadsheet? (with more powerful processing rate?)

Well, there's what we get...

Is seeing believing? or do we rule by our left brain?
Hm... do you agree with what the computer has "said" from 111,111,111 x 111,111,111 onwards?