First, our number has digit**s**, so it must be **greater than 10**.

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

Third, 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?

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