Had a look at the question? Got a paper and pen handy? Let’s take a look at the answer!
The answer
First:
Our number has digits, so it must be 10 or greater.
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?