Can a classification tree model "know" to predict only one of every class for many subsets in a data?

In order to help recipients understand my question, there will be context added. I don't know a whole lot of semantics so please bare with me. Draper is hosting a competition on Kaggle to classify images by day. The chosen metrics were overall-brightness and the number of similarities between images taken on different days. In addition, the "compared" variable was used as a categorical variable.