Posted by JohnX2 on May 12, 2002, at 0:40:00
In reply to Re: My Solution to Lights and Switches » JohnX2, posted by Ron Hill on May 11, 2002, at 22:48:04
Yes you are brilliant Ron. And you don't burn your hand.My brain fart, I typed this up quickly and couldn't remember
the details off the top of my head. I should have had the restriction
that only 1 lever could be turned on at a time. I should have thought
a little more about the possibilities for solutions for my quiz
as stated! I personally didn't try to solve it the straightforward way,
I wonder if I would have figured it out...hmmm.I guess it makes it more fun...having 2 solutions.
You and Manda are co-champs. Sorry, skimping on e-bucks.
- John
> > Do you want to go ahead and post your solution out of altruism. Or are you still holding out for the $$$$s ?
> -----------
>
> John,
>
> Enclosed is my solution to the originally stated brain teaser (i.e. without the freedom to touch the light bulbs).
>
> ~~~~~~~~~~~~~~~~~~~~~~
> STATEMENT OF PROBLEM:
>
> Inside a room there are 4 lamps sitting on a table (A-D).
>
> Outside the room there are 4 levers (1-4).
>
> Each lever can turn on or off one of the lamps (i.e.
> when all 4 levers are on all 4 light bulbs will be on).
>
> There is a closed door to the room (seperating the levers
> from the lamps).
>
> You can turn on the levers in any position you want (on/off),
> and then open the door to observe the lamps (which ones
> are on).
>
> Your goal is to figure out which lever control which lamp.
>
> *Caveat*: You have only *2* trials to change the levers and then
> observe the behavior of the lamps in the room.
>
> How do you solve the problem?
>
> (If you've heard this before, hold the answer to your chest).
>
>
> ------------------------------------
>
> Inside room:
>
> Lamp-A Lamp-B Lamp-C Lamp-D
>
> --Door---------------------------------
>
> outside room:
>
> Lever-1 Lever-2 Lever-3 Lever-4
>
>
>
> ~~~~~~~~~
> SOLUTION:
>
> 1. Configure switches, on and off, as follows;
>
> SW-1 on
> SW-2 off
> SW-3 on
> SW-4 off
>
> 2. Open the door and record the on/off status of each light bulb.
>
> 3. Close the door and reconfigure the switches, on and off, as follows;
>
> SW-1 off
> SW-2 off
> SW-3 on
> SW-4 on
>
> 4. Open the door and record the on/off status of each light bulb.
>
> 5. From these collected data, one can calculate the particular one-to-one correspondence between switches and bulbs. In other words, which switch operates which bulb.
>
> John, to demonstrate that the algorithm works, randomly select a connection correspondence between switches and bulbs {e.g. (1, B), (2, C), (3, A), (4, D)}, and then, using your selected (secret) correspondence, determine which bulbs are lit in Steps 2 and 4 as instructed above. Send me (post) this information and, in return, I will tell you which switch operates which bulb.
>
> In other words, tell me which bulbs light when the switches are configured, firstly, as:
>
> SW-1 on
> SW-2 off
> SW-3 on
> SW-4 off
>
> And, secondly, as
>
> SW-1 off
> SW-2 off
> SW-3 on
> SW-4 on
>
> And, in return, I can tell you which switch operates which bulb.
>
> -- Ron
poster:JohnX2
thread:23447
URL: http://www.dr-bob.org/babble/social/20020509/msgs/23602.html