The circuit is simple. Each image wheel has a disk (it’s the white Delrin with red letters) attached at the other end of the axle, in the back of the cabinet.

On this disk (the side you can’t see) is attached a single magnet. The other wheel has the identical setup. (Note: this is not the magnets you can see on the outside of the wheel; they serve a different purpose discussed later.) On the mount in front of the white disk is an array of six reed switches, one for each planet or (for the other disk) moon. When the images on the wheels are lined up properly, the magnets on these disks will pick up one of six sets of two reed switches in series that tells the circuit a correct guess has been made. Initially, I made this circuit with a good old-fashioned DPDT relay. The problem was that the relay was so LOUD that the visitor could determine which answer was correct simply by spinning the wheel until the relay picked up. To solve this problem, I decided to go solid state. I used the standard 4077 NOT gate and 74HC32 AND gate. The circuit is pictured below:

If the wheels are properly aligned:

Both reed switches are closed. The NOT gate gets 5V and goes LOW on output; AND gate #2 gets one 5V input. If the “Check Answer” button is pressed, AND gate #2 gets a second input and the “Correct!” LED lights.

If the wheels are NOT properly aligned:

At least one reed switch is open, the NOT gate gets no input and goes HIGH on output. When the “Check Answer!” button is pressed, AND gate #1 gets a second input, and the “Try Again!” LED lights. Here is a picture of the very simple and inexpensive circuit: