Answers are whited out.

#1: Open the door and see which lamps are on or off. Alternate flipping the switches and looking through the door to find out which switch connects to which light. Just don't go through the door.

#2: Fill the five-gallon bucket with water, then fill the three-gallon bucket from the five-gallon bucket. Once the three-gallon bucket is full, there will be two gallons left in the five-gallon bucket. Empty the three-gallon bucket. Pour the two gallons from the five into the empty three-gallon bucket, then fill the five-gallon bucket again. Fill the remaining gallon of space in the three-gallon bucket, and the five-gallon bucket will now hold four gallons of water.

#3: If X=Y, then subtracting Y squared in the second step is just setting the equation to 0=0, since both variables have the same value. X^2-Y^2 is the same as X^2-X^2; if the first statement is true.

Answers are whited out.

 

#1: Open the door and see which lamps are on or off. Alternate flipping the switches and looking through the door to find out which switch connects to which light. Just don't go through the door.

 

#2: Fill the five-gallon bucket with water, then fill the three-gallon bucket from the five-gallon bucket. Once the three-gallon bucket is full, there will be two gallons left in the five-gallon bucket. Empty the three-gallon bucket. Pour the two gallons from the five into the empty three-gallon bucket, then fill the five-gallon bucket again. Fill the remaining gallon of space in the three-gallon bucket, and the five-gallon bucket will now hold four gallons of water.

 

#3: If X=Y, then subtracting Y squared in the second step is just setting the equation to 0=0, since both variables have the same value. X^2-Y^2 is the same as X^2-X^2; if the first statement is true.

1. I should have specified that once you open the door, you can't flip the switches. Sorry.

2. Yep

3. That still doesn't disprove the validity.

I've already heard the answer to number one (flick on the first switch and leave it for five minutes, then turn it off and turn on switch two and rush into the room. Whichever lightbulb is hot is number one, the lit one is two, and the off one is three), so let me give you these alternate solutions:

1) Use your power drill to drill a hole throw the door big enough to see inside so that you know which switch operates which light.

2) Take your screwdriver and unscrew the electrical panelling so you can follow the wiring from the switches to the lamps.

3) Find the electrician who set up these lamps and ask him. If he won't tell you, use your drill and screwdriver to make him tell you.

We already have an answer for two, so I'll skip over that.

And number three I learned in math class: YOU DIVIDED BY ZERO!!!!