wu :: forums
« wu :: forums - Light Bulbs And Switches Variation 2 »

Welcome, Guest. Please Login or Register.
Dec 1st, 2020, 9:29pm

RIDDLES SITE WRITE MATH! Home Home Help Help Search Search Members Members Login Login Register Register
   wu :: forums
   riddles
   easy
(Moderators: towr, ThudnBlunder, william wu, Icarus, Eigenray, SMQ, Grimbal)
   Light Bulbs And Switches Variation 2
« No topic | Next topic »
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print
   Author  Topic: Light Bulbs And Switches Variation 2  (Read 9622 times)
alien2
Uberpuzzler
*****






   


Gender: male
Posts: 6918
Light Bulbs And Switches Variation 2  
« on: Oct 13th, 2020, 3:10am »
Quote Quote Modify Modify

You are in a room with sixteen* light switches, each of which controls one of sixteen (incandescent) light bulbs in the next room. Your task is to determine which switch controls which bulb. All lights are initially off, and you can't see into one room from the other. You are allowed only two chances to enter the room with the light bulbs. You must close the door each time you enter or leave the room with the light bulbs. How can you determine which light switch goes with which light bulb?
 
* I modified the riddle. Instead of 11 there's 16 light bulbs.  
« Last Edit: Oct 26th, 2020, 6:22am by alien2 » IP Logged


rmsgrey
Uberpuzzler
*****





134688278 134688278   rmsgrey   rmsgrey


Gender: male
Posts: 2837
Re: Light Bulbs And Switches Variation 2  
« Reply #1 on: Oct 13th, 2020, 3:01pm »
Quote Quote Modify Modify

If I can distinguish 4 with one visit, I can distinguish 16 with two visits (and sufficient time).
IP Logged
alien2
Uberpuzzler
*****






   


Gender: male
Posts: 6918
Re: Light Bulbs And Switches Variation 2  
« Reply #2 on: Oct 13th, 2020, 3:25pm »
Quote Quote Modify Modify

Check out the big brain on rmsgrey! I am still stuck at 11 bulbs.
IP Logged


rmsgrey
Uberpuzzler
*****





134688278 134688278   rmsgrey   rmsgrey


Gender: male
Posts: 2837
Re: Light Bulbs And Switches Variation 2  
« Reply #3 on: Oct 14th, 2020, 11:15am »
Quote Quote Modify Modify

on Oct 13th, 2020, 3:25pm, alien2 wrote:
Check out the big brain on rmsgrey! I am still stuck at 11 bulbs.

 
In general, if you can distinguish between n cases in one test, two tests will let you distinguish between n2.
 
For example, in a scenario with 4 cases, call them A, B, C and D, there are 16 possible outcomes from the two tests:
 
AA, AB, AC, AD
BA, BB, BC, BD
CA, CB, CC, CD
DA, DB, DC, DD
 
For a simpler example with light-bulbs, if you can only distinguish 2 cases - on and off - then in two visits you can identify up to 4 bulbs with their switches: label the switches 0, 1, 2 and 3. Before your first visit, turn off 0 and 1, and on 2 and 3. Before your second visit, turn off 0 and 2, and on 1 and 3. On your visits, for each bulb, jot down a 1 if it's lit; a 0 if it's not (putting later labels for each bulb directly to the right of earlier labels). After the two visits, you'll have written down a binary number for each bulb, corresponding to the switch that controls it.
IP Logged
alien2
Uberpuzzler
*****






   


Gender: male
Posts: 6918
Re: Light Bulbs And Switches Variation 2  
« Reply #4 on: Oct 14th, 2020, 11:28am »
Quote Quote Modify Modify

You're right. One can discern 16 light bulbs. There are four groups with each group consisting of four light bulbs you discern on your 1st visit.  
 
 
« Last Edit: Oct 15th, 2020, 3:32am by alien2 » IP Logged


Grimbal
wu::riddles Moderator
Uberpuzzler
*****






   


Gender: male
Posts: 7508
Re: Light Bulbs And Switches Variation 2  
« Reply #5 on: Oct 25th, 2020, 12:51pm »
Quote Quote Modify Modify

You need only one visit.
 
Turn all switches off.  Turn the first switch on, wait a month, turn the second switch on, wait a month, etc. until the last.  Then go to the room and observe in which order the bulbs burn out over the next few months.
 
That's all!
IP Logged
alien2
Uberpuzzler
*****






   


Gender: male
Posts: 6918
Re: Light Bulbs And Switches Variation 2  
« Reply #6 on: Oct 26th, 2020, 5:00am »
Quote Quote Modify Modify

Sure. And if you're Superman all you need is a couple of seconds since you've X-Ray vision and you can see through the walls. -_-
IP Logged


rmsgrey
Uberpuzzler
*****





134688278 134688278   rmsgrey   rmsgrey


Gender: male
Posts: 2837
Re: Light Bulbs And Switches Variation 2  
« Reply #7 on: Oct 26th, 2020, 11:22am »
Quote Quote Modify Modify

on Oct 25th, 2020, 12:51pm, Grimbal wrote:
You need only one visit.
 
Turn all switches off.  Turn the first switch on, wait a month, turn the second switch on, wait a month, etc. until the last.  Then go to the room and observe in which order the bulbs burn out over the next few months.
 
That's all!

 
Google tells me that the typical lifespan of an incandescent bulb is 1000 hours - or 6 weeks. So, after 15 months of turning on one switch per month, you'd expect 14 bulbs to already be burnt out by the time you go through - maybe only 13.
IP Logged
towr
wu::riddles Moderator
Uberpuzzler
*****



Some people are average, some are just mean.

   


Gender: male
Posts: 13725
Re: Light Bulbs And Switches Variation 2  
« Reply #8 on: Oct 28th, 2020, 11:27am »
Quote Quote Modify Modify

And the variation will probably mess it up.
 
There a lightbulb that has been burning almost continuously for over a hundred years  
https://en.wikipedia.org/wiki/Centennial_Light
IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
rmsgrey
Uberpuzzler
*****





134688278 134688278   rmsgrey   rmsgrey


Gender: male
Posts: 2837
Re: Light Bulbs And Switches Variation 2  
« Reply #9 on: Oct 28th, 2020, 12:13pm »
Quote Quote Modify Modify

on Oct 28th, 2020, 11:27am, towr wrote:
And the variation will probably mess it up.
 
There a lightbulb that has been burning almost continuously for over a hundred years  
https://en.wikipedia.org/wiki/Centennial_Light

 
That light pre-dates the Phoebus Cartel - which, among other things, set the standard lifespan of an incandescent bulb to 1000 hours, fining manufacturers who produced bulbs that lasted longer.
IP Logged
towr
wu::riddles Moderator
Uberpuzzler
*****



Some people are average, some are just mean.

   


Gender: male
Posts: 13725
Re: Light Bulbs And Switches Variation 2  
« Reply #10 on: Oct 29th, 2020, 11:57am »
Quote Quote Modify Modify

That cartel ceased operations in the second world war. And I see no mention they enforced a minimum life expectancy. I also very much doubt they fined based on maximum life of a light bulb.
 
page 5 on of this document has an example distribution based on empirical data.
It's close enough to a normal distribution for arguments sake, with a pretty significant standard deviation. (Although there are better fitting distributions, like log-normal.)
 
So basically, time-to-failure will not be a reliable method to find out which bulb is controlled by which switch.
« Last Edit: Oct 29th, 2020, 12:03pm by towr » IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print

« No topic | Next topic »

Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright © 2000-2004 Yet another Bulletin Board