First, our number has digits, 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?