Can brain training reduce falls?

Probably not.

I just read an interesting article connecting brain training (and the lack of scientific proof that it works) with issues regarding aging and the elderly.

http://brainblogger.com/2014/12/02/if-brain-training-wont-help-the-elderly-what-will/

The article suggests that other factors may be far more effective at creating a healthier brain than supposed brain training exercises.

For instance, cognitive decline is associated not only with a reduction in mental exercise but also with reductions in physical activity, sleep, and proper nutrition. Nutrition in particular is often overlooked as a critical component of brain health, even though certain nutrients are required for the maintenance and growth of the very brain cells that support cognition. In addition, brain changes that occur with age do much more than promote cognitive decline. They also alter peoples’ moods and behaviors, and helping Grandma feel less depressed may improve her quality of life more than helping her remember where the remote control is. (emphasis added)