These are few patterns which may be obvious for Maths enthusiasts and also there is a formulae based proof but neverthless pretty fascinating when we see how these play out
a) 111 x 111 = 12321
11 + 1 = 12 and 12x12 = 144 which is 123+21
b) 112 x 112 = 12544
11+2 = 13 and 13x13 = 169 which is 125+44. Not only that this number is more unique for the following reasons
11-2 = 9 and 9x9 = 81 which is 125-44! (we don't see that in the earlier example due to a very standard formulae based logic
c) 113x 113 = 12769
11+3 = 14 and 14x14 = 196 which is 127+69
d) 114x114 = 12996
11+4 = 15 and 15x15 = 225 which is 129+96
This pattern doesn't repeat when we go the series starting with 12 or 13. Can someone figure out why this is happening?
a) 111 x 111 = 12321
11 + 1 = 12 and 12x12 = 144 which is 123+21
b) 112 x 112 = 12544
11+2 = 13 and 13x13 = 169 which is 125+44. Not only that this number is more unique for the following reasons
11-2 = 9 and 9x9 = 81 which is 125-44! (we don't see that in the earlier example due to a very standard formulae based logic
c) 113x 113 = 12769
11+3 = 14 and 14x14 = 196 which is 127+69
d) 114x114 = 12996
11+4 = 15 and 15x15 = 225 which is 129+96
This pattern doesn't repeat when we go the series starting with 12 or 13. Can someone figure out why this is happening?
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