One of my older son’s homework problems asked him to find 3 digit multiples of 7 whose digit sums were also multiples of 7. I was puzzled by this problem had it on my mind most of the day today.
I hoped that talking through it would help me understand what the math idea was behind the problem. Sadly no, but we still had a good talk.
Here’s the problem and the work my son did:
So – still quite puzzled about the problem – I decided to see if there was anything quirky that came up looking at a divisibility rule for 7 with 3 digit numbers. This gave us a nice opportunity to talk about modular arithmetic:
Finally, since I wasn’t making any progress seeing the point of the original problem, I had him talk about other divisibility rules that he knew:
So, a nice conversation, but I’m actually baffled. I’ll have to ask the author of the problem what he was trying to get at – I feel like I’m missing the point.
Mike's Math Page 
maybe there was no point at all, and trivial solutions were ok.