The famed "brain-training" company Lumosity would like its users to believe that brain games and puzzles "exercises" the brain and promote brain health. This sounds intuitive enough: we should exercise the brain if we want the brain to get stronger, right? To this, scientists say no. In fact, most would agree that to boost memory, thinking skills, and other cognitive prowess, we should actually be exercising the body.
The benefits of exercise extends to many organs, the brain notwithstanding. Regular aerobic exercise promotes blood flow and the production of anti-inflammatory chemicals. Furthermore, exercise can stimulate the release of growth factors that appear to boost neuronal survival and even spur the formation of new blood vessels. Combined, scientists have documented that exercise can boost the size of the hippocampus, which is responsible for memory and learning.
By contrast, scientists have not documented any such physical benefits of being sedentary while "brain-training" with puzzles and games. If a person spends a lot of time doing crossword puzzles or other logic problems, they would likely get very good at such tasks. However, it is unlikely improvements in those specific brain tasks would also carry to memory and learning overall.