When any user presses their button, the CAP line will go high. As buttons always 'bounce', there will be a whole raft of pulses in the first few milliseconds before the contacts in the button settle down. IC1A is configured as a monostable that drives the CK line - this will go low for about 100mS when the monostable is triggered.
Remember that 4013 RS flip-flops are positive edge triggered, so when IC1A times out, the CK line will go high. If any button is still pressed, the BNx line will be latched through to its Q output (see IC2A above), turning on its relay.
At the same time, IC1B will latch the CAP line to its Q output. If any button is pressed, this will cause IC1A's RESET input to go high, forcing the CK line low regardless of any other pulses on the CAP line, thus debarring other users who may subsequently press their buttons, i.e. IC1A's monostable cannot be fired again until the RESET button is pressed. This mechanism ignores noise spikes and bounces on any button line, and completely blocks other users once the first user has pressed their button.
The only way one or more outputs may be triggered at the same time is if the users press their buttons within IC1A's timeout period (about 100mS), thus indicating a draw. Because of the high noise immunity of the circuit, you can use multi-core cable to connect the control unit to the users' boxes.
Each box requires 4 wires - two of these, GND and Vcc (+12VDC) are common to all boxes; the other two are the users' BNx and LTx lines. The BNx line needs to be connected via a push-button to the Vcc line, and some 12V MES bulbs (or similar) need to be connected between the LTx line and GND.
As these sorts of systems are generally used by two teams of up to 4 users , I placed the two user connectors at each end of the PCB. These are standard IDC 2x5 box headers on a 0.1" matrix. I then used 10-core cable to each group of 4 user boxes, with the Vcc and GND wires being daisy-chained through and dropping out a pair of BNx and LTx lines in each box.
The cable from the control unit to the first box was 2M long, and the cable between each box in a chain was 1M. The quiz master can then sit at the control box between the teams. It should be noted that all users are equal - the system doesn't differentiate between users, so the split is for typical conveniance only; 8 teams of 1 user or 4 teams of two are equally valid combinations.
Alternatively, you can easily add more users (see below) to have 2 teams of 10 etc.