How to set up 40 hz flashing LED lights to light a room?
As noted by Peter Camilleri: This might help sufferers of Alzheimer's disease, and I certainly hope it does, but it may cause problems for other people.

Generating a 40Hz square wave is not difficult. The simplest solution would likely be an astable 555 timer circuit. You could also use a microcontroller, but that is a significant hassle in comparison. Note that the 555 can only output 200mA, so you may need to put a transistor on the output to drive your light.

LED is probably the best choice for the light source. The filament in an incandescent bulb will remain hot and luminous briefly after it is switched off. At 40Hz, the overall effect might be more like a dim bulb than a flashing bulb. An LED will turn on and off abruptly. 

One light is probably better as well, just because you won't have to have power wiring throughout the room for distributed lights. A single high power LED can provide significant illumination. 

Think battery power, like a USB power bank. There are significant electrical safety problems associated with powering things from the mains, especially if the user is suffering from Alzheimer's disease. You want your system to present no hazard to the user.

This circuitry is relatively small and simple, so you could assemble it on stripboard/veroboard.

I would do it this way.
USB Power Bank -> Astable 555 timer -> Driver transistor -> Light

Here is a calculator for the 555: http://www.ohmslawcalculator.com/555-astable-calculator