The more intense instrument for the brain is the piano, because you use both hands, a foot, and the other senses. It really gives your brain a full workout. However, chess would be good for tactical thinking.
Those help with vocab, reading, and memory/problem solving. A good exercise, but not so much on the mathematical side. However, every bit helps. An instrument that requires more interaction, especially when reading music is a full brain work out.
How about Sudoku
Even though it uses numbers, it can just as easily be played with letters or other symbols. However, it does exercise problem solving as well, different then crosswords, so it is a good exercise. The reason playing an instrument is the best is because you read music, use appendages, calculate timing, count, and listen all together. The calculations and counting are more mathematical and help that portion of the brain. Different puzzles can help different areas of the brain. Tetris was found to improve memory in one study for those who played 30 min a day for a month. There are different separate practices, but the ultimate is playing an instrument. If you sing and read music this also benefits the brain, but not to the extent of playing an instrument. An instrument isn't the only way to engage, it just engages more portions of the brain. Playing different types of puzzles, games, singing, and reading can be effective as well, but are less complete as a single activity. The instrument I play only has 4 valves so is less intensive on the motor cortex, but still engages it.
Yeah I guess
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