Switch A turns lights 1 and 2 on/off or off/on
Switch B turns lights 2 and 4 on/off or off/on
Switch C turns lights 1 and 3 on/off or off/on
Switch D turns lights 3 and 4 on/off or off/on

+-----+       +-----+
|  1  |       |  1  |
| OFF |       | OFF |
+-----+       +-----+
|  2  |       |  2  |
| OFF |       | ON  |
+-----+       +-----+
|  3  |       |  3  |
| OFF |       | OFF |
+-----+       +-----+
|  4  |       |  4  |
| OFF |       | ON  |
+-----+       +-----+

FIGURE 1      FIGURE 2

Switches D, B, C and A are thrown in turn with result that Figure 1 turns into Figure 2. Each cell represents a given light and its state.

One of the switches does not work at all. Which one?

Flipping all four switches should toggle each light twice.  So it they all start OFF they should all end OFF.
The fact that 2 and 4 are ON means they did not get toggled twice because Switch B does not work.

Posted by Jer on 2014-10-20 08:48:17