### Brain Teasers

# 9 Times the Sum

There is a number that is 9 times the sum of its digits. What is this number?

### Answer

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## Comments

1

how can 1 be the same as 9 times 1 Cathal?? Wrong!

Cathal is right. 9 is nine times greater than 1.

you are mistaking 9*1=1. there is a difference.

you are mistaking 9*1=1. there is a difference.

I disagree with you, Mad-Ade. The teaser states that the number (in this case, one) must equal nine multiplied by the sum of all its digits. In this case, the number one has one digit. Nine multiplied by one does not equal one. Mad-Ade, would you please explain how you are right?

You won't get a response, Piffle. I don't know what Mad and Cath are thinking, but the teaser is just fine the way it is.

Of course it is correct! If the units digit is x and the tens digit is y then the number is 10y+x. The sum of its digits is x+y. So 10y+x=9(x+y) leading to y=8x. Since they must be single digits then x=1 and y = 8. Unless of course you want to consider the trivial solution zero.

It was an interesting quiz, but I believe there should have been an explanation with the answer.

The explanation is that the number must be a multiple of nine. All multiples of nine have digits that sum to a multiple of nine. Therefore the answer must be 9 x 9 = 81.

At least that's how I did it.

At least that's how I did it.

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