The spotlight puzzle

A conference room contains three separate wall-mounted spotlights - right, left and front of stage. Each is controlled by its own on-off switch. These three switches are numbered 1, 2 and 3, but they are in a back-room which has no sight of the the spotlights or the conference room (and there are no reflections or shadows or mirrors, and you are alone). How do you identify each switch correctly - right, left, front - if you can only enter the back-room once?

Answer
Switch on number 1 and leave it on for 30 seconds, then switch it off. Switch on number 2 and leave it on. Enter the conference room. The spotlight that is on is obviously number 2. The spotlight that is warm is switch 1, and the other spotlight is number 3.

Utilities puzzle

Draw three houses in a horizontal row. Draw three utilities suppliers beneath them: Gas, Water, Electicity. You should now have six points or boxes on your sheet of paper or flip chart. The challenge is to connect each house to each utility supplier without any of the nine connection lines crossing.

Answer
This classic puzzle which has been around for hundreds of years, although it was obviously not known as the Utilities Puzzle until relatively recently. Strictly speaking it is impossible to solve the puzzle using two dimensions on flat piece of paper; there will always be a minimum of two crossed connections.

There are however two great lateral thinking solutions:
1. Take the final line (that would otherwise cross another) through the utilities and/or houses themselves, which unless specifically outlawed in the instructions would not constitute a cheat.
2. The puzzle can be solved without taking any lines through buildings, if the utilities and houses are on the outer surface of a ring torus (three-dimensional doughnut) shape. You can create the torus effect simply by making a hole in the paper centrally between all six connection points and folding flaps around the edges of the hole and the edges of the sheet, so as to take certain lines through the hole and around the back of the sheet to make the connections.