Mindbender 1

 

I regularly do the Mindbender mathematical puzzles in the Western Morning News. Usually they involve fairly simple algebra, but sometimes they need number theory. This one proved even more difficult than usual. The problem comes down to finding a number that's one more than 17 times the sum of its digits. I did solve it eventually, but by a lot of intuitive jumps. Can anyone see a straightforward method? Have a go, and then go here (spoiler with solution) to compare.

- Ray