Which resistor to use for blue led

alnath:
you get this page :
blue led
and you'll see that there is already an internal resistor, thus it needs to be powered at 12V (not 5V)

Well no, it doesn't.

If you do look at the datasheet, you will see that it is specified for a minimum of 4V, so it just does not shine quite as bright at 5V as it does at 12.

It is presumably - deliberate. They are "idiot-proofing" the kit, including parts that are difficult to damage by unfortunate mistakes, such as connecting directly across the power supply. I wonder whether the other colour LEDs are the same?

alnath:
If the led is designed for 12V, you'll have to use a transistor or a FET (included in the kit) to drive it from Arduino.

Likewise, not really.