There are a lot of different riddles that, when solved, can give the player an opportunity not only to advance further but also to learn something new and interesting in Undertale.
Most of the riddles the player can find are at the location called Waterfall. For example, one of them is Undertale Piano Puzzle. To solve it, the player needs to find another room where the statue stands. In order to see which keys will need to be pressed, you need to give the statue the umbrella that you get before. After that, you need to return to the musical instrument and play the melody, the notes of which you had to memorize.
After this puzzle is solved, the main protagonist will gain access to another room, where he has the opportunity to meet another character named Annoying Dog. So by the way, developer Toby Fox introduces himself to the game.