Solution+1

Solution for Problem Solver #1

Keep the first bulb switched on for a few minutes. It will get really warm, right? So all you have to do then is switch it off, switch another on, walk in the room with the bulbs, touch the two that are off, the one that was switched on will still be warm, and the other will be the one that has never been turned on.

Solution for Problem Solver #2

|| 1 || 2 || 3 || 4 || 5 || 6 ||
 * 6 || 12 || 24 || 48 || 96 || 192 ||
 * 6 || 18 || 42 || 90 || 186 || 378 ||