DoodleLearning logo

What is the only number that is exactly twice the sum of its digits?

Had a look at the question? Got a paper and pen handy? Let’s take a look at the answer!

The answer


Our number has digits, so it must be 10 or greater.


Our number cannot be greater than 36 (since the maximum value of each digit is 9, and 2 x (9 + 9) = 36.


Our number must be even (since it’s been doubled.)

So, a search of our even numbers between 10 and 36 yields the solution 18. Alternatively, the algebraic solution can be written as: Let the first digit be ‘a’ and the second digit be ‘b’:

10a + b  =  2(a + b)

10a + b  =  2a + 2b

8a        =   b

Since  a and b are digits, they can only take whole number values between 0 and 9 – this makes the only valid solution to be a = 1 and b = 8. The algebraic solution has the advantage that it is easily applied to the extension of this problem, i.e. three times, four times, five times or n times the sum of its digits.

Can you find the only value of n (between 2 and 9) that has a multiple solution?

Related posts


Are you a parent, teacher or student?

Get started for free!

Are you a parent or teacher?

Student Login

Which programme would you like to use?

Log in to DoodleCoaching

If you’d like to use Doodle’s browser version, please visit this page on a desktop.

To log in to Doodle on this device, you can do so through our apps. You can find out how to download them here: