Fw: Lightbulb stumper...
"Robert J. Brown" (rj@eli.elilabs.com)
Thu, 23 Oct 1997 15:33:31 -0500
>>>>> "caryle" == caryle clear <cpcj@sprynet.com> writes:
caryle> (Had to forward: put .com instead of .org!) Ok, first
caryle> off, anyone who has heard this before, please let the
caryle> others have some fun with it for a while before I give
caryle> the answer!!! Here's the situation: You are in a
caryle> room (A) which contains ONLY three switches. In another
caryle> room (B) there are three lightbulbs which are
caryle> controlled by the switches in room A. You CANNOT
caryle> see into room B from room A. (ie, no windows, mirrors,
caryle> etc. can't see the light from bulbs either.).
caryle> Once you leave room A, you may NOT re-enter--game's over!
caryle> Q---How do you determine which switch operates which
caryle> bulb??? Anneliese
First, you must determine whether there is a one to one correspondence
between switches and controlled bulbs. This is in fact highly
unlikely under random conditions, as each bulb is potentially
independent of the others, yet a combination of more than one switch
could affect a single bulb. THE PROBLEM STATEMENT DOES NOT RULE OUT
THIS POSSIBILITY!
With 3 switches, we have 3 boolean state variables as inputs. With 3
bulbs, we have 3 switching functions of 3 inputs as the overall
output. Since there are 2^(2^n) switching functions of n inputs,
there are 2^(2^3) = 2^8 = 256 different ways a single bulb could be
affected by the set of 3 switches. With 3 bulbs, we may choose 3
switching functions from this set, giving a total of 256^3 =
16,777,216 possibilities, or over 16 million, to choose from.
Even if I *COULD* see all the bulbs, I wouldn't touch this one with a
ten foot pole!
--
-------- "And there came a writing to him from Elijah" [2Ch 21:12] --------
Robert Jay Brown III rj@eli.elilabs.com http://www.elilabs.com 1 847 705-0424
Elijah Laboratories Inc.; 37 South Greenwood Avenue; Palatine, IL 60067-6328
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