You said 9?

Number Theory Level 2

Look at the pattern below: $\begin{aligned} 9 \times 1 = 9 & & & & \color{#3D99F6}9 = 9 \\ 9 \times 2 = 18 & & & & \color{#3D99F6}1 + 8 = 9 \\ 9 \times 3 = 27 & & & & \color{#3D99F6}2 + 7 = 9 \\ \cdots & & & & \color{#3D99F6}\cdots \end{aligned}$

Is it true that all multiples by 9 (except $9 \times 0$ ), the sum of its digits will be always 9?

Note: For example, the sum

3 + 6 + 9 = 18

, you need to sum the digits until your answer be a digit, so

1 + 8 = 9.

Yes No

1 solution

Bibhor Singh
Dec 23, 2017

You can take any multiple of 9, the sum of its digits will always be 9. I have tried up to 999,999,999,999,999,999

You said 9?

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