You are in a windowless room with one door and 4 light switches in the off position. One of the switches controls a light bulb in another room which you cannot see. The other three switches do nothing. You may manipulate the switches however you wish, but once you leave the switch room to go to the light bulb room you cannot go back. How can you determine which switch controls the light bulb?
2006-06-14 20:43:24 · 16 answers · asked by Scott R 6 in Science & Mathematics ➔ Mathematics
This can be solved.
The door is closed.
The lights are all in the off position. The light is initially off.
2006-06-14 20:51:15 · update #1
Many of you are not reading the problem carefully.
2006-06-14 20:53:43 · update #2
Is Eulercrosser the only competent mathematician who reads these things?
2006-06-14 20:57:45 · update #3
ASIDE TO "bequalming":
Logic is a branch of mathematics. In fact, the two are so intertwined as to be virtually isomorphic concepts. Read "Principia Mathematica" by Russell & Whitehead. Just about every concept in the universe can be explained with mathematics.
2006-06-15 06:27:23 · update #4
turn on the first 2 switches let them sit for a little while. then turn on the 1st and 3rd switch. go into the room right away, if the bulb is hot but off that means it was the 2nd one (because the switch is now off but it had to be on) if the bulb is cold still (not really hot) it was the third one because the light just turned on and the 1st one didn't turn it on at all if it is not on and the bulb is not hot at all it was the fourth because you never touched that switch it was on and hot then it was the first because it was on long enough for the bulb to get hot.
so... when only the 1st and 3rd swith was on (after turning off 2)
1=if it was on and hot
2=if it was off and hot
3=if it was on but cold
4=if it was off and cold
2006-06-14 21:08:34 · answer #1 · answered by ♥ The One You Love To Hate♥ 7 · 4⤊ 2⤋
DA BEARS has the first logically correct answer (assuming the bulb heats up). Eulercrosser's solution is good, but you have to be able to determine if the bulb is "really hot" or "kind of hot," not knowing how hot the bulb will get if left on for 10 minutes, and further not knowing if the bulb will cool down entirely after 10 minutes of being off.
Further, Eulercrosser didn't really read the question because his first statement asks if the bulb is off when the question specifies that all switches are in the off position.
Finally, this is a logic problem, not a math problem.
2006-06-15 04:52:17 · answer #2 · answered by bequalming 5 · 0⤊ 0⤋
Is the light off before you start?
Turn on one switch for about 10 minutes. Then turn it off and turn a second switch on for ten minutes. After the second 10 minutes, turn the second switch off and turn a third switch on. Now go into the room.
If the light is on, then it's the third switch.
Assume the light is off:
Touch the bulb. If it is warm, then it was the first switch, since the bulb would be very hot if it was on for 10 minutes and had no time to cool down.
If it is hot, then it is the second switch (as just explained).
If it is cold, then it is the fourth switch, since the light was never turned on.
No.
2006-06-14 20:49:08 · answer #3 · answered by Eulercrosser 4 · 0⤊ 0⤋
Call the light switches A, B, C, and D.
Turn light switch A and B on and leave them on for a few minutes. Then turn A off, and turn C on and go to the room immediately.
If the light bulb is off, but it is hot to the touch: it is A
If the light bullb is off, but cold to the touch: it is D
If the light bulb is on, and hot to the touch: it is B
If the light bulb is on, and not very hot to the touch: it is C
2006-06-14 22:39:41 · answer #4 · answered by phyziczteacher 3 · 0⤊ 0⤋
Doesn't matter, just turn all on. Since three out of four switches does nothing at all, just treat the four switches as one and control the light on and off by control all four together everytime
2006-06-14 20:51:08 · answer #5 · answered by RT 3 · 0⤊ 0⤋
You can't. You need two observations to eliminate 3 candidates.
PS
We do read the questions, and you do need two observations as stated above. You have assumed that the light is of a kind that gets warmer the longer it is left on and that it can be reached. In this case your second observation of the two required is its temperature. However, the question as stated does not allow for this assumption; you must assume this second measurement cannot be made unless the question allows for it.
2006-06-14 20:49:38 · answer #6 · answered by Epidavros 4 · 0⤊ 0⤋
You didn't say the door is open or closed. I will assume open - so flip the switches and look through the door for light.
2006-06-14 20:48:01 · answer #7 · answered by happyharrytick 3 · 0⤊ 0⤋
"Is Eulercrosser the only competent mathematician who reads these things?"
Could you explain the math behind this. I am interested in becoming a competent mathematician! Did the person in the dark room bring his calculator with him, or did he do all this math in his head?
2006-06-14 20:58:13 · answer #8 · answered by Cliffo 3 · 0⤊ 0⤋
you turn one on leave it on for a whille, then turn it off, then turn another one on, and go into the room, if the light is hot, but off, it was the first switch, if the light is on, it is the second, if the light is off and cold it is the third one
2006-06-14 20:52:16 · answer #9 · answered by slayergurl90 2 · 0⤊ 0⤋
i would say turn on a switch for a few minutes... turn it off and repeat with the other switches... go to the other room and touch the lightbulb... depending on how hot or cold it is, you can estimate which switch had triggered it....
2006-06-14 20:48:15 · answer #10 · answered by deathblooms7894 5 · 0⤊ 0⤋