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 2 years ago
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
 2 years ago
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

This Question is Closed

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1Sounds 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

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1you 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

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5Consider 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 !

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1oh 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

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5For intellectual profit of the community (not fun, god forbid that !)

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1so you know the answer. Now I'm more interested in this puzzle

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0Yo @Mikael what's up!! ... serves as bookmark.

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5There is a follow up problem  which HAS practical serious applications and is very deep

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1what 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

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5Glad to see you \[ YodaNot , \bf @ganeshie8 \]

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0:) so the state has to be communicated to all the 100 robots, but the bulb has only two states hmm

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5The 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.

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5Ok let's make it simpler:

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5How each robot can be sure with probability of \[p= 1 10^{6}\] that all others HAVE visited the bulb  devise a method for that.

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5@Algebraic! you are missed here , one needs some critical approach...

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5Each robot has also a secondscounting watch

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5Well let's say @ChmE is "warm" in his attempt...

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1I'm still thinking I see the problem you mentioned

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5Just devise an approach with lower possibility of that

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1can 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

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1and my first method will be complete in 100^101/100! years. lol

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5Great 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

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5I mean  the bulb , in some sense is a thirdrate "bolt"

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1the 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.

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5OK  push forward on the path of SIMPLIFYING !!!

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5"the first turns it off"....

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5and ignore (for a sec) the actual numbers of seconds

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1I will continue to think about it. Gotta catch a bus

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5So gentlemen and ladies  who's up to the challenge ?!

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.0I'm going to stay quiet for a while since I've seen the problem before (in slightly different terms).

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5\[\bf \text{here is Second Problem  will be posted after this one is done and cleared.}\] \[\bf \color{red}{\text {Now the robots have to somehow}\,\,\\ {\Huge\color{green}{Choose \quad a \quad president}}\\{\text{EXACTLY IN THE SAME SITUATION }} }\]

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5No tricks  real new democratic choice of president.

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1the 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

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1if 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

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5All right  so here is The second problem. \[ \bf \text{Choosing a specific number by majority of votes.} \\ \text{ Each robot has has own number known to all.}\\ \text{ Using all of the above they have to choose one pf them.}\\ \text{He will be called the president.} \]

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1Check my soln to problem 1. I think I've got it

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5@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"

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1OMG!!! I swear I didn't cheat. Been thinking about this question on and off all day yesterday

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5But you were a bit unclear  you have to STATE that he turns it off during 99 opportunities he is given

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5By the way  he does know  but how do the others know that he DOES know ?

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1the robot knows but how to the other robots know he knows?

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5First robot counted 99 lighton and reached the conclusion that all have been at the bulb. NOW  how will he communicate that fact to all the others ?

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1haha. This isn't fun anymore. I gotta think about this

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5This 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 turningoff guy was right before them is too low.

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1ok. thx. Is this a question that was proposed to you in one of your classes?

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5Thanks  now let us call here the other people who has been here  so they appreciate our work. @bahrom7893 @sauravshakya @kingGeorge, @ganeshie8 @hartnn @experimentex

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5Welcome to our humble abode Mrs @sauravshakya @hartnn and all !

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.0ACTUALLY THIS SIMILAR PROBLEM WAS ALREADY SOLVED BY ME TOO.

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.0THAT IS THE SIMILAR QUESTION....... only number are different..AND ITS LOGICAL NO SERIES

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.0AS far as I remember.

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.0ya, i have also seen such problems...

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5Dear 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

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5Because I have met this situation in real life engineering problem.

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5Best of luck. and keep them cool and well nutritioned !

siddhantsharan
 2 years ago
Best ResponseYou've already chosen the best response.0Haha. Yeahh. Thanks. Nice problem though.

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1I 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.

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.5It is assumed the do communicate and agree beforehand.
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