Balsa was trying too build a shed but realised that to do so, she needed to cut up a board. After trying and failing to cut the board correctly, she then asked Professor Layton to try and make a solid square out of two pieces of the board. After he had done so, she thanked him and gave him a screw part as a thank you. She then asked Layton to help her out with another board problem, to which he helped her out again. Amazed that he had solved her another one of her problem's, she thanked him and gave him a battery to show her gratefulness.
Balsa, like other residents of Dropstone, gives Professor Layton and Luke a couple puzzles during their time in town. The puzzles she gives you are "Board Splitter 1" and "Board Splitter 2".
You may have met Balsa in Dropstone, where she was probably building something. A hardy woman who enjoys physical labor, she lets her husband, Gabe, do most of the cooking. For his birthday, she built a display case for his ramekin collection.