need help taking one LED from RGB 5050 strip, also remote and voltage questions

So I have an RGB 5050 LED strip.  It's cutable every three lights.  I need just one LED.  So I'm figuring (correct me if I'm wrong, because I'm a total newbie to this) that I need to solder the 3 pins on one side together, and put a resistor on each of the other pins (with the red getting the resistor that's a different value).  Problem is, I don't know which pins are which.  There's a little mark on the corner of the LEDs; do I put the resistors on this side, or the other side? 

This strip is meant to be used with 12 volts.  Also pictured is a remote with receiver and a mini controller (I will use one or the other).  These are also for 12 volts.  I'd like to use them with less.  I tested with a 9 volt battery, and that worked.  3 volts did not work, not sure why.  I haven't yet tried 6 volts.  Is there anything about the controllers that requires more voltage, or is it an issue with the LEDs?  I do not have any specs on the LED strip, but don't pretty much all LEDs work with a 3 volt coin cell?   Since the resistors were being used for all three LEDs, how does it impact things when I switch to just one LED? 

I also took apart an LED candle that has a similar remote, and it was also meant to run on 12 volts.  It works perfectly on 3.   I would just use this, but sadly its round shape doesn't fit.

Any help is very much appreciated.  Thanks.

edit:  Just tested with the remotes, 3 LED strip, and 6 volts, and only the red LED works.

Picture of need help taking one LED from RGB 5050 strip, also remote and voltage questions
The strip is designed so that the 3 LEDs are wired in series. Then each strip of 3 are connected together in parallel. This way each section needs 12V to run and with each additional section you just require more amperage from the power source. It doesn't surprise me that you can get the single strip to run on 9V but it's designed for 12V.

Now you should be able to remove 2 of the LEDs without a problem. But you will need to figure out the wiring of the LEDs so you can bridge the right contacts. Take a good hard look at the PCB and see where each trace goes. Then try to draw out a schematic of how everything is wired. This will help you determine how to go about removing the LEDs. Unless you want to just remove a Single LED and attach it directly to the controller board. But you will need to figure out what resistors you'll need for a single LED. Might be hard without knowing the specs of the individual LED.

Another note, a single LED may be able to run on only 3V but the controller board will not. As you have found the controller board will run on as low as 9V. But it won't take long for a battery to drop just below that and start causing problems.

If the candle is too big for a necklace then how is this other setup going to be any better. You will require more power to run it meaning a much larger battery pack. So while the new solution may be slimmer it will be much much thicker.