Minecraft Java Edition – How to Make a Logic Gate with 4 Inputs and One Output in Minecraft Redstone

I think what you really want is rising and falling edge detectors. You're only concerned when the first light detector goes high, and when the first light detector goes low, and not so concerned with the state of the other light detectors. From there, you can wire them into an RS NOR latch.

Since simply wiring all the outputs of the light detectors together is equivalent to ORing them, you'll only need one rising edge detector. Have that feed into the SET input of the latch. You'll also have to feed the output of each detector into their own falling edge detector, and from there wire all of them into the RESET input of the latch.

You'll also have to isolate the outputs of the light detectors from each other leading into the rising edge detector, but that's easily accomplished using a repeater.

UPDATE:
After tooling around in creative, there are some additional things that I noticed. First, I had to use a pulse extender on the reset input to the RS NOR latch (I used the sticky piston version). Secondly, the delays I used for the edge detectors is slightly different than what is in the wiki. As with a lot of redstone circuits where timing is important, it's usually necessary to adjust the delay on the repeaters to get everything to work properly. Finally, if combining the signals from the various light detectors before passing them through the edge detectors, you may notice that a set or reset doesn't toggle the latch. This is very unlikely in a light detector since all of them should change states before any change back.

As promised, here are some MCEdit schematics. They aren't the prettiest, but they're functional.

I think the answer from MBraedley is correct: the best way to handle this scenario (allowing access to a single player at a time) would be to use Command Blocks to teleport one player into and out of your quiz area. You can program a Command Block to teleport the nearest player to a set of coordinates like so:

/tp @p x y z

I don't know what would happen if two players somehow managed to be the exact same distance from the command block (i.e. does just one get teleported, or do they both get teleported since there is a tie for the "closest"). This additional argument may be necessary to limit it to only one player:

/tp @p[c=1] x y z

The next step is to create a circuit whereby clicking an "entry" button will teleport one player into the quiz area, deactivating this button so that it cannot teleport anyone else in until the player exits the quiz area by clicking a second "exit" button, teleporting them out. Here's one such example circuit I just threw together in my survival game:

The blue blocks are buttons that feed their signals into AND gates (green blocks). The outputs of the AND gates will activate Command Blocks (shown here as redstone lamps at the bottom of the image) and will also feed into the input of a T flip-flop circuit (red blocks). The output of the toggle circuit runs behind the red blocks and feeds into an input of each of the AND gates.

When the toggle circuit is in the "off" state (no output, as shown in the image) then the signal from the right button is disabled and the right redstone lamp (i.e. Command Block) cannot be activated. Activating the left button will cause the left redstone lamp to activate and immediately flip the toggle to the "on" state. This will subsequently disable the signal from the left button and reenable the signal from the right button.

This circuit should give you the ability to allow one player at a time to teleport into your quiz area via a button press. Once they reach the end they can then press another button to teleport out and reactivate the entry button for the next player. I'd also suggest enclosing the circuitry and your quiz area in bedrock, so your average player can't mess with any of it.