compensate for missing leds
You can measure U (forward voltage) of one of the existing LEDs (with a multimeter). If you disconnect one of the 100 Ohm resistors from a working chain, you can measure I (current), too. In fact, you need not disconnect -- simply measure the voltage across the resistor, and use Ohm's Law to work out the current. With that information, you can either buy new LEDs to replace the missing ones, or alter the resistors and bridge the missing LEDs.