What does the circuit look like to switch two lights using two switches into four different states?

Question

At my workplace there's a room with two entrances, each featuring a push button light switch, A and B. There are two ceiling mounted lights, 1 and 2.

Switch A switches both lights on/off. Funny enough, if both lights are on, switch B switches off a single light (2). Now in this state, switch A "flips" the state of the two lights (2 goes on, 1 goes off).

| SW-A | SW-B || LAMP1 | LAMP2 |
+------+------++-------+-------+
| on   | on   || on    | on    |
| off  | on   || off   | off   |
| on   | off  || on    | off   |
| off  | off  || off   | on    |
+------+------++-------+-------+

I don't know if these are 3-way or 4-way switches.

Just out of academic curiosity: how exactly is this - obviously flawed - circuit possibly implemented?

(Disclaimer: I'm a physician, not any kind of engineer)

Answer 1

Rewriting your truth table a little more succinctly:

| SW-A | SW-B || LAMP1 | LAMP2 |
+------+------++-------+-------+
| on   | on   || on    | on    |
| off  | on   || off   | off   |
| on   | off  || on    | off   |
| off  | off  || off   | on    |
+------+------++-------+-------+

^{simulate this circuit – Schematic created using CircuitLab}

Figure 1. Mis-wired two-way switching circuit.

Does this fit?

In Europe this is referred to as a two-way switching circuit. In the US the switches are referred to as 3-way as they have three wires.

It looks like LAMP1 is wired to the wrong terminal on the switch.

Answer 2

Possible connection scheme (you have given partial information so this may not be correct)- SWA and SWB are '3-way' (by North American definition) switches

^{simulate this circuit – Schematic created using CircuitLab}

With switches in the shown configuration, SWB turns LAMP2 on and off, LAMP1 is on. SWA will turn both lamps on or both lamps off.

However with SWB in the opposite position, LAMP2 is off and LAMPa is on. Flipping SWA will reverse that (LAMP2 on and LAMP1 off).

To fix this, change the wiring to SWB so the lamps are in parallel, though I'd be tempted to leave it just to confuse people.