8 - 3mm 3V LEDs
1/4" wood base
22gauge wire (red and black)
$0.20 number puzzle (took awhile, but can be found at most party stores in the prizes section).
Then the back side of the tiles were painted with the conductive paint. The inside of the red frame was coated with the conductive paint where the 1 and 15 tiles would be also. At the same time, I drilled two 1/16th inch holes in the wood where the number 1 and 15 tiles would be when they were all in order. The 8 holes along the edge of the wood base for the LEDs were drilled at this time as well.
After that, the LEDs were placed in the holes. I bent the positive wires down to both hold the LEDs in the holes while i was working and to distinguish the two wires for each one, so that I wouldn't solder the wrong wires together.
I decided to run all of the LEDs parallel with a 3V power source because that is what they're rated and they would not light up as well if run in a series with the same power source. To have them all running parallel, I merely soldered all of the positive wires from the LEDs together (red wires) and connected them to the power source. Then, all of the negative wires were connected and went through the number game 'switch' and then that connects to the negative side of the power source.
Step 3: Final Step
As you can see from the pictures, the LEDs won't light up until you have the tiles in the correct order. You can also see a bit of the conductive paint where the 15 tile should go.