Little Solver is just starting to work for Scout Kid. I got it about six months ago along with Little Finder. Both apps are intended for older children, but both can work for toddlers with some parental involvement. Little Finder is great for an under-two as long as you're willing to read the clues to them, but Scout Kid is just in the last month or so beginning to work out how Little Solver works.
It's basically figural analogies that increase in complexity as you answer them correctly. Scout Kid doesn't really answer them correctly often enough to advance a level yet, but that's fine. I'm confident repetition will teach him to begin recognising the patterns that I explain to him for each question, as it generally does in a toddler's life. And, figural analogies for a two-year-old? Not too shabby. $0.99.