Were you allowed a calculator? If so, I have an excellent brute force method that will take seconds. If not, my method will still work but will take minute or two longer to manually calculate.
Since 55 is relatively small number, it has many multiples within any range of 1000. So it really doesn't matter what the first three digits are in terms of divisibility. So I pick the highest possible 3: 989xxx. Consequently, I intend to find the lowest 7 digit multiple of 55 and work backwards from there. I find that the factor that yields this lowest 7 digit number is 1 000 000 / 55 = 18181.81818...
So the factor multiplied with 55 to form POPLAR is probably a few hundred integers under that. (because there is a minimum difference between 1000000 and 989xxx of 10000, I reuse the above calculation 10 000 / 55 = 181.818...)
So the factor is maximum 18181 - 181 = 18000.
18000 x 55 = 990000
17999 x 55 = 990000 - 55 = 989945. But P and L have the same values, so this is not the multiple
17998 x 55 = 989945 - 55 = 989890. But P and A have the same values, so this is not the multiple
And keep on going down the list and come to:
17995 x 55 = 989725.
So P + O + P + L + A + R = 9 + 8 + 9 + 7 + 2 + 5 = 40
I know this method is very crude. I would like to know if there is a better way of doing this.