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Re: My Solution to Lights and Switches » JohnX2

Posted by Ron Hill on May 11, 2002, at 22:48:04

In reply to Re: Who's in charge of handing out the prizes? » Ron Hill, posted by JohnX2 on May 10, 2002, at 19:11:05

> 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


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