It would be conceivable to make led’s that only operate at a specific voltage because of some internal circuitry.

It’s also possible that the 9v battery has some “extras” stuffed into it as well.

I vote for custom trick wire; logic dictates that the 3 LED’s are on 3 different circuits (for the series video). Why couldn’t you spin 3 (or more) threads of motor coil wire together (which is coated in insulator) with patches of exposed wire to make the circuit? Note that the wire used is silver, and quite thick (like solid core).

I vote custom made wire containing 3 insulated cores. Very clever stuff. Bravo.

I suspect each LED secretly has a band pass filter soldered underneath it. They switches are changing the frequency of the circuit causing the correct LED to light up. It still baffles me that all three can light up, unless each switch can make a narrow band of spectrum corresponding to each LED.

What if the battery is actually giving out an AC supply? The parallel circuit would just require a diode in the switch to ground out the unwanted polarity.

AC might also help the series find a solution too, at work so I don’t have time to diagram it all out.

The clue is in the fact there are only two LED’s
The switches are coils (possibly capacitor tuned too), diode rectifier and switch combos.
One LED’s and one of the “switches” are backwards :D
The 9volt does nothing :D
Well that’s the way I would do it :D

Either that or frame by frame video editing as it is clearly not fixed to the table which was my first idea (through holes in the table, unlikely)

Probably a One-wire signaling variant.
Addressable LEDs.
Switches are not just switches, but rather, signaling devices which turn on/off their associated LED.

Not even looking at the schematic that was on the table I notice a few problems with this.
In the first video looking at how he solder the series. All switches would need to be on for the leds to light and if one switch is off none of the leds would light. The switches are simple spst rocker switches. in one position the prongs are in a open postion (off) in the other postion the prongs are in a closed postion (on). And there is one thing as well. the leads he used to connect everything is solder. When he solder the strand to the pieces is stayed a strand. Solder melts when touched with the high concetrated heat of a iron. the solder should not act that way.
the biggest clue to me in the first video is at one point the entire color correction/setting of the video changes. It dulls down slightly. Also looking at how the leds look when lit. there are discrepancies of how they should look. The light spread on the table. it only goes two way. One, if the led was lighting the table the color would not be pure red since the color of the table is green. Second, the type of leds he used are front emitting diodes. all the light comes out the front. and since the leds are facing up we should not see splash light on the table.

In the second video there is the same problem with the solder. again there is the side splash and look at the led on the right. when it lights it has the same intensity as the left. yet its angle is slightly away from the camera. so there should be a slight noticeable difference.

conclusion. Video is faked. After Effects was used to add the light of the leds. there are too many problems to suggest that this is real. as for the AC idea. its a 9v battery. there is no AC battery. Batteries are DC and to achieve AC you would need a converter.

There is another version of same circut over here:
http://www.spryciarze.pl/zobacz/jak-zbudowac-prosty-obwod-szeregowy

same author,
author promised that there is no special effects, everything is explainable.
he said that he will reavel shortly how is working.

The original author claims on YT that
1) all wires and soldering points are real
2) no video editing has been done

Notice that in both the serial and in the parallel circuit the leds are shining even bright, no matter how many are lit. This smells multiplexing.

I could get the parallel circuit to work with a microcontroller in a setup similar to charlieplexing (so, no AC needed).

In order to determine which LED should be on, first the switches need to be read. This could be done by adding a capacitor in series inside the switches and using the microcontroller as a capacitance meter.

Here is what I mean:
http://oi44.tinypic.com/2ibyxyh.jpg

Regarding the circuit with leds in series: still thinking on this one. Help me…

Im pretty sure i have an idea of how he is doing the series video…and im just going to leave this here… http://www.phy.bnl.gov/pp2pp/alekseev/mv6461a.pdf

Nice Trick, i like it.
Maybe its the half cycle trick mentioned earlyer for two of the leds. The third led is actually a led lookalike light bulb, which needs a certain voltage to light up, and the switch corresponding Switch is, when in off position, a resistor that drops the voltage below the voltage needed by the light bulb. The leds are one with integrated voltage regulator.
I know there are light bulbs that look like leds, but i hove no idea how to make it light only at a certain voltage.
I hope its not a stupid idea, its way to late to be sure. No wait, its to early to be sure now.

PS: It was mentioned that the third led to is controlled by ac trickery, i know, but would it work too?

Definetly based on something like this:
http://www.nemetzpower.de/ELO/ParadoxonELO1278.pdf

Anybody noticed the black band (rubber iso.-tape)on the lower end of the battery?
Battery is hacked for shure.
No idea about the third led.

Respect, anyway.

The “parallel” circuit seems to fairly well explained by others as simply using an ac source and diodes to bypass the switches when they are open.

For the series I think I’ve come up with a solution that only requires a standard ac source, and only uses diodes:
Troll_series

My solution has one led powered on the negative cycle of the supply. The other two have zener diodes places in front of them to block the current if the voltage is below some threshold. The zener diode on the first led has a higher breakdown voltage than the one on the second.
Likewise the voltage drop across the first two bybass diodes (on the switches) are different.
I think this setup could work if the appropriate values were selected for each of the diodes.
Not sure if all of the components could be hidden inside the switches and LEDs though.