My son was working on a few old AMC 10 problems yesterday and problem 17 from the 2016 AMC 10a gave him some trouble:
I thought this would be a nice problem to go through with him. We started by talking through the problem to make sure that he understood it:
In the last video he had the idea to check the cases with 10 and 15 balls in the bucket, so we went through those cases:
Now we tried to figure out what was happening. He was having some difficulty seeing the pattern, so I spent this video trying to help him see the pattern. The trouble for me was that the pattern was 0, 1, 2, . . ., so it was hard to find a good hint.
Finally he worked through the algebraic expression he found in the last video:
This isn’t one of the “wow, this is a great problem” AMC problems, but I still like it. To solve it you have to bring in a few different ideas, and combining those different ideas is what seemed to give my son some trouble. Hopefully going through this problem was valuable for him.