To start with 12544 is a perfect square and I always find perfect squares having lot of unique attributes
a) 12544 - 112 x 112
b) 125 - 44 = 81 which is 9 x 9
c) 125 + 44 = 169 which 13 x 13
d) Now 9 + 13 = 22 and 13 - 9 = 4; Now look at the square root which is 112 (11 + 11 = 22 and 2 + 2 = 4)
How many squares exhibit this kind of pattern? Can we explore further?
Few more interesting attributes
e) Go back to 12544 and add some of the digits: 144 + 25 = 169 which is again 13 x 13 and 144 is 12 ^ 2 and 25 is 5 ^ 2 (12 and 5 are the first 3 digits of 12544)
f) Now look at 112 again - 11 x 11 = 121, 2 x 2 = 4. 121 + 4 = 125 (which is the first 3 digits of 12544 again)
a) 12544 - 112 x 112
b) 125 - 44 = 81 which is 9 x 9
c) 125 + 44 = 169 which 13 x 13
d) Now 9 + 13 = 22 and 13 - 9 = 4; Now look at the square root which is 112 (11 + 11 = 22 and 2 + 2 = 4)
How many squares exhibit this kind of pattern? Can we explore further?
Few more interesting attributes
e) Go back to 12544 and add some of the digits: 144 + 25 = 169 which is again 13 x 13 and 144 is 12 ^ 2 and 25 is 5 ^ 2 (12 and 5 are the first 3 digits of 12544)
f) Now look at 112 again - 11 x 11 = 121, 2 x 2 = 4. 121 + 4 = 125 (which is the first 3 digits of 12544 again)
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