$111...11^2$

Algebra Level 1

$\large \underbrace{111\ 111\ 111^2}_{\text{Number of 1 = 9}} = ?$

2 solutions

Arifin Ikram
Oct 3, 2019

$1²=1$

$11²=121$

$111²=12321$

$1111²=1234321$

This is a sequence. So our answer will be $111111111²=$ $\boxed{12345678987654321}$

This Question is more likely to be about "Number Theory", If you could change the topic it'd be great.

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Prakash Kallanmarthodi - 1 year, 8 months ago

Prakash Kallanmarthodi
Oct 7, 2019

This is a theorem for squaring numbers which only contains 1 in every single digit

Count how many "1's" there are and writing all the numbers from 1 to the amount (Value of how many digits there are) and back. 1²=1

11²=121

111²=12321

1111²=1234321

11111²=123454321

111111²=12345654321

1111111²=1234567654321

11111111²=123456787654321

111111111²=12345678987654321

By the way, this theorem only works for numbers under 9 digits