Odd Ones

Algebra Level 1

1 * 1 = 1
11 * 11 = 121
111 * 111 = 12321

What will the middle number be if one were to multiply 111111111 * 111111111?

The answer is 9.

2 solutions

Tom Dufall
Jul 27, 2014

You can see the pattern, by looking at the 3 examples, then apply it to the question.

$1 \times 1 = 1$ the 1st is the highest, with 1 (1 digit squared)

$11 \times 11 = 121$ the 2nd is the highest, with 2 (2 digits squared)

$111 \times 111 = 12321$ the 3rd is the highest, with 3 (3 digits squared)

In each of the examples we're increasing the number of digits in the number we squared by each time, and if 'n' is the number o f digits in the number we square, the highest digit in the solution is the 'n'th digit, with a value of 'n'.

Therefore for the 9th value $(111111111 \times 111111111)$ the answer is simply 9.

Heder Oliveira Dias
Jul 23, 2014

(111111111)^2 = 12345678987654321 then the middle number is 9.

OP should replace the word 'number' to 'digit'.

Btw, it can be proved that the middle digit of the number $\underbrace{111\ldots111^2}_\text{N ones}$ is equal to $N$ . So you don't have to square the whole number to find out the middle digit as you did.

mathh mathh - 6 years, 10 months ago

It is very clear from the pattern that answer would be 9 I think we neednot square 111111111

Tina Mittal - 6 years, 10 months ago

Odd Ones

The answer is 9.

2 solutions

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