This is what I came up with.
Unfortunately, this project has a sad ending.
Step 1: The Circuit
The whole thing is simple in concept - the three judges each have a button to push when they are fed up with a contestant.
As each button is pressed, in any order, that judge's light comes on. When the third light is lit, a buzzer sounds and the contestant is ejected from the stage.
The switches required are Double Pole Single Throw (DPST) switches that latch (stay on until they are pushed again). Double Pole Double Throw (DPDT) switches will also work, you just don't use all the connections.
The switches I used were guitar-effect foot-pedal switches (DPDT) I bought from ebay. I chose these because I knew who was going to be a judge, and I expected the switches to be pressed with some gusto.
Step 2: Breadboard? We Don't Need No Stinking Breadboard!
Lemonie's diagram shows standard bulbs, but I wanted to use a pile of salvaged LEDs. That meant I needed to get everything the right way round.
I soldered lengths of wire to the switch contacts. Four to each switch, two on each side.
I then taped the switches to a ruler, and knitted everything together following the diagram.
Step 3: The Box.
I bought a sheet of 6mm MDF board (about one fifth the price of the equivalent in real wood) and built a box to sit on a table in front of the judges.
The sheet was 1220mm x 610mm (4x2 feet), which meant that the box I made was 1220mm long, 100mm high and 200mm front-to-back.
I made three sides with the MDF, and used blocks of spare timber to make the ends rigid. The whole thing was hot-glued together for speed, and to "caulk" the gaps left by my wobbly jigsaw cuts. I also added strips of 20mm square timber I had spare, just to hide the hideously ugly joins at the corners.
I drilled holes in the top for the switches (they came with nuts and washers to fit them into a panel), and clusters of holes in the front for the LEDs.
Step 4: Putting the Two Together.
However, I decided that single LEDs were not bright enough for the job, so I made clusters of five - 10mm LEDs in the centre of a square of four smaller LEDs.
To make the clusters, I soldered groups of five LEDs in parallel with small lengths of wire.
I fitted the switches, slotted the LED clusters into their holes (hot-glued in place, second picture), and then connected the whole thing together with more wire (last picture).
I tested the whole thing worked before doing the final soldering of the longer wires, and taped wires and joints to the inside of the box to prevent damage in transit.
Step 5: The End Never Came...
The plan was for the organisers to paint the box to match the stage-set.
Unfortunately, due to circumstances beyond our control, the show didn't happen, and then they closed the school...
The box is now sitting in the corner of my storage shed, waiting patiently for another school to need it...