anonymous
  • anonymous
First problem 100 thinking robots are given a challenge : they will communicate only by means of a single light bulb which can be either in the state 1 (light on) or in state 0 (light off). Each second a randomly chosen \[\bf ONE \quad single \] robot can see the bulb (others don't- in that second) and keep it in the previous state or change it to opposite state. Bulb is On at first. Each second one chosen randomly out of 100. The challenge is to know -WHEN every one of them has been at the bulb at least once (or more) times. This info has to reach all of 100 eventually. SEE THE SOLUTION BELOW
Mathematics
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
Sounds like a statistics problem. To me there will always be a chance the same robot doesn't see the bulb, but it will be so small it's considered 0. We have to decide how small is too small. I really can't help any further then relaying my thoughts. sry
anonymous
  • anonymous
you could set up a limit as x approaches 0 for the last robot. But i don't know how to do that for this problem
anonymous
  • anonymous
Consider it given that there does occur a visit of each to the bulb. THIS IS NOT THE QUESTION !! The question is to communicate that event AFTER IT HAPPENNED JUST USING THE BULB !

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
oh ok. I did read it wrong. Is this a question you need an answer to, or a question for fun to the community? I would have to think about this for a while. still not much help
anonymous
  • anonymous
For intellectual profit of the community (not fun, god forbid that !)
anonymous
  • anonymous
Hi there @experimentX
anonymous
  • anonymous
so you know the answer. Now I'm more interested in this puzzle
experimentX
  • experimentX
Yo @Mikael what's up!! ... serves as bookmark.
anonymous
  • anonymous
There is a follow up problem - which HAS practical serious applications and is very deep
anonymous
  • anonymous
what if the first robot turns the bulb off and every robot you sees the bulb and it is their first time will turn it on. If it is their second time will turn it off. If the bulb is left off for a long time then we can assume every bot has seen it. I don't know how to determine the length of time
anonymous
  • anonymous
Glad to see you \[ Yoda-Not , \bf @ganeshie8 \]
ganeshie8
  • ganeshie8
:) so the state has to be communicated to all the 100 robots, but the bulb has only two states hmm
anonymous
  • anonymous
The offered method has weakness - a robot doesn't know whether it was a multiple visit by some group that made the light off (if that is his observation) or the complete set of visits.
experimentX
  • experimentX
lol .. .thanks!!
anonymous
  • anonymous
Ok let's make it simpler:
anonymous
  • anonymous
How each robot can be sure with probability of \[p= 1 -10^{-6}\] that all others HAVE visited the bulb - devise a method for that.
anonymous
  • anonymous
@Algebraic! you are missed here , one needs some critical approach...
anonymous
  • anonymous
Each robot has also a seconds-counting watch
anonymous
  • anonymous
Well let's say @ChmE is "warm" in his attempt...
anonymous
  • anonymous
I'm still thinking I see the problem you mentioned
anonymous
  • anonymous
Just devise an approach with lower possibility of that
anonymous
  • anonymous
So ..
anonymous
  • anonymous
can a robot leave a bolt. so the first time they visit they leave a bolt and there is a robot that collects all the bolts when he has 100 including his own they are done
anonymous
  • anonymous
and my first method will be complete in 100^101/100! years. lol
anonymous
  • anonymous
Great beginning of BRAIN -STORMING , NOW that you have "I wish" method - try making "the bolt" only with the ligh on/Off and the conditions given
anonymous
  • anonymous
I mean - the bulb , in some sense is a third-rate "bolt"
anonymous
  • anonymous
the first turns it off. and he counts how many times he see it on. The other robots turn it on one of their 2 cycles.
anonymous
  • anonymous
OK - push forward on the path of SIMPLIFYING !!!
anonymous
  • anonymous
"the first turns it off"....
anonymous
  • anonymous
and ignore (for a sec) the actual numbers of seconds
anonymous
  • anonymous
I will continue to think about it. Gotta catch a bus
anonymous
  • anonymous
So gentlemen and ladies - who's up to the challenge ?!
KingGeorge
  • KingGeorge
I'm going to stay quiet for a while since I've seen the problem before (in slightly different terms).
anonymous
  • anonymous
\[\bf \text{here is Second Problem - will be posted after this one is done and cleared.}\] \[\bf \color{red}{\text {Now the robots have to somehow}\,\,\\ {\Huge\color{green}{Choose \quad a \quad president}}\\{\text{EXACTLY IN THE SAME SITUATION }} }\]
anonymous
  • anonymous
No tricks - real new democratic choice of president.
anonymous
  • anonymous
the 1st robot turns it off and he only ever turns it off. Every other robot turns the light only once. If they have already turned it on they leave it off or if it is on they leave it on. The 1st robot counts how many times he turns it off til 99
anonymous
  • anonymous
if the robots see the light on but havent touched it then they leave it on til they are given the chance to turn it on
anonymous
  • anonymous
All right - so here is The second problem. \[ \bf \text{Choosing a specific number by majority of votes.} \\ \text{ Each robot has has own number known to all.}\\ \text{ Using all of the above they have to choose one pf them.}\\ \text{He will be called the president.} \]
anonymous
  • anonymous
Check my soln to problem 1. I think I've got it
anonymous
  • anonymous
@ChmE This seems the solution "the 1st robot turns it off and he only ever turns it off. Every other robot turns the light only once. If they have already turned it on they leave it off or if it is on they leave it on. The 1st robot counts how many times he turns it off til 99"
anonymous
  • anonymous
OMG!!! I swear I didn't cheat. Been thinking about this question on and off all day yesterday
anonymous
  • anonymous
But you were a bit unclear - you have to STATE that he turns it off during 99 opportunities he is given
anonymous
  • anonymous
ok
anonymous
  • anonymous
By the way - he does know - but how do the others know that he DOES know ?
anonymous
  • anonymous
what do you mean by that
anonymous
  • anonymous
the robot knows but how to the other robots know he knows?
anonymous
  • anonymous
First robot counted 99 light-on and reached the conclusion that all have been at the bulb. NOW - how will he communicate that fact to all the others ?
anonymous
  • anonymous
haha. This isn't fun anymore. I gotta think about this
anonymous
  • anonymous
This is NOT fun, but i will spare you this time : Only probabilistically they will know. How? by seeing the light in their SEVERAL personal visits off they conclude that the probability that the FIRST - the turning-off guy was right before them is too low.
anonymous
  • anonymous
ok. thx. Is this a question that was proposed to you in one of your classes?
anonymous
  • anonymous
Thanks - now let us call here the other people who has been here - so they appreciate our work. @bahrom7893 @sauravshakya @kingGeorge, @ganeshie8 @hartnn @experimentex
anonymous
  • anonymous
Welcome to our humble abode Mrs @sauravshakya @hartnn and all !
anonymous
  • anonymous
Much appreciated !
anonymous
  • anonymous
ACTUALLY THIS SIMILAR PROBLEM WAS ALREADY SOLVED BY ME TOO.
anonymous
  • anonymous
http://mathriddles.williams.edu/?p=146
anonymous
  • anonymous
THAT IS THE SIMILAR QUESTION....... only number are different..AND ITS LOGICAL NO SERIES
anonymous
  • anonymous
AS far as I remember.
hartnn
  • hartnn
ya, i have also seen such problems...
anonymous
  • anonymous
Dear visitor @sauravshakya - I bet you ten sayings of praise (of your choosing) that the following you have NOT solved before http://openstudy.com/study#/updates/50631053e4b0583d5cd34249
anonymous
  • anonymous
Because I have met this situation in real life engineering problem.
anonymous
  • anonymous
Thanks Highlander ....!
anonymous
  • anonymous
Hey @siddhantsharan
anonymous
  • anonymous
Hello. :)
anonymous
  • anonymous
Best of luck. and keep them cool and well nutritioned !
anonymous
  • anonymous
Haha. Yeahh. Thanks. Nice problem though.
anonymous
  • anonymous
I was just thinking @Mikael . How is my solution/our solution correct because it relies on the robots communicating prior to seeing the lightbulb? Which by the given conditions cannot happen.
anonymous
  • anonymous
It is assumed the do communicate and agree beforehand.

Looking for something else?

Not the answer you are looking for? Search for more explanations.