Ron and Devil,
To see why each string of LEDs should have their own current-limiting resistor, look at this simulation which shows the effect of connecting individual LEDs (or strings of series-connected LEDs) in parallel. I purposely choose two different types of LEDs which have different forward voltage drops to connect in parallel. Note in the upper trace plane that when a single current-limiting resistor feeds paralleled LEDs, one LED I(D1) gets all of the current, while I(D2) gets none. In the lower panel, each LED has its own current-limiting resistor, and viola, now the both LEDS get a current dependent only on their own Vf and respective resistor.