Answer to The Case of the Curious Cakes

The criminal mastermind has two children, one aged seven and the other aged nine. There was only enough cake mixture for two number-shaped cakes, so that suggests two young children with single-digit ages. Because there are 16 candles, there are only two possible answers: The kids must either be twins aged eight (two eights are 16), or they are not twins, with their ages being seven and nine (which adds up to 16). The second phone call referred to one of the children as being "younger", indicating that the kids were not twins, so they must be seven and nine.