How to calculate the number of blades?
Determining the number of blades is one of the steps in designing the main rotor of a helicopter, but not the first one. The main rotor design process is an iterative process with quite a few input parameters, which depend on the mission type:


Max. TO weight
Max. speed
Installed engine power
Autorotation performance
Noise
Manoeuvring g
Blade profile
Blade area
Vibratory loads


Using these inputs, the design process determines:


Rotor diameter. This determines the disk loading: lower disk loading results in better hover performance and auto-rotational performance, higher disk loading in better cruising flight performance.
Tip speed. As close as possible to the drag divergence speed in cruise, also a limiting factor in selecting rotor diameter.
Rotor solidity. How much disk area is actually occupied by blade area, determined by blade stall limits in manoeuvres. Increasing the rotor solidity requires more engine power, but increases the blade stall margin.
Number of blades. Mostly based on dynamic criteria, less on aerodynamic ones. The Bell 212 shows that rotor solidity can be increased by using wider blades, but using more blades minimises vibratory loads and the noise per blade passing.


The rotor design process is quite broad, and can best be found in the theory books which also contain statistical data to aid the initial stages. The plot below is from Leishman and shows that light helicopters have a blade length of about 4 meters, apparently a good length for this weight and mission type.



The overlapping twin rotor disks of the Chinook result in one rotor operating in the wake of the other, reducing efficiency and requiring more disk area. So total disk loading will reduce.

Two good books on helicopter stuff: Helicopter Aerodynamics, Stability and Control by Ray Prouty, and Principles of Helicopter Aerodynamics by J. Gordon Leishman.