Four Logic Puzzles

1. Light Switches

A working light bulb is in a closed room with no windows. Outside the room, is a panel of three switches, one of which controls the light inside (up is on, down is off.) You may do anything you like to the three switches and then enter the room to inspect the light. After this, without any further experimentation, you must indicate which switch controls the light. What do you do?

2. There is a cactus that blooms in the Mojave Desert that is so fragrant and beautiful that people come from all over the world to catch a glimpse of its flowers. Itââ?¬â?¢s called the Night-blooming or Starlight cactus. It blooms only by the clear soft light of the stars, and only on cloudless nights. It produces small, white, star-shaped blooms in five-minute intervals: one blossom at the end of the first five minutes to exposure, two blooms in the next five minutes, three in the third five, and so on till sunrise, when they all vanish. If you were lucky enough to watch the Starlight cactus one night for six hours, how many blossoms would you see?

3. You fell asleep while watching the Starlight cactus bloom? How could you do that? After four hours, you fell asleep for an hour? How many blossoms did you actually see bloom?

4. Three painters can paint six fences in 3 hours. (The fences are all the same size.) How many fences can seven painters paint in five hours?