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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
 one year ago
 one year 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
 one year ago
 one year ago

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ChmEBest ResponseYou've already chosen the best response.1
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
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
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
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
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 !
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
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
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
For intellectual profit of the community (not fun, god forbid that !)
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
so you know the answer. Now I'm more interested in this puzzle
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
Yo @Mikael what's up!! ... serves as bookmark.
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
There is a follow up problem  which HAS practical serious applications and is very deep
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
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
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
Glad to see you \[ YodaNot , \bf @ganeshie8 \]
 one year ago

ganeshie8Best 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
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
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.
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
Ok let's make it simpler:
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
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.
 one year ago

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

MikaelBest ResponseYou've already chosen the best response.5
Each robot has also a secondscounting watch
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
Well let's say @ChmE is "warm" in his attempt...
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
I'm still thinking I see the problem you mentioned
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
Just devise an approach with lower possibility of that
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
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
 one year ago

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

MikaelBest ResponseYou've already chosen the best response.5
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
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
I mean  the bulb , in some sense is a thirdrate "bolt"
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
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.
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
OK  push forward on the path of SIMPLIFYING !!!
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
"the first turns it off"....
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
and ignore (for a sec) the actual numbers of seconds
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
I will continue to think about it. Gotta catch a bus
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
So gentlemen and ladies  who's up to the challenge ?!
 one year ago

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

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

MikaelBest ResponseYou've already chosen the best response.5
No tricks  real new democratic choice of president.
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
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
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
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
 one year ago

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

ChmEBest ResponseYou've already chosen the best response.1
Check my soln to problem 1. I think I've got it
 one year ago

MikaelBest 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"
 one year ago

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

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

MikaelBest ResponseYou've already chosen the best response.5
By the way  he does know  but how do the others know that he DOES know ?
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
the robot knows but how to the other robots know he knows?
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
First 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 ?
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
haha. This isn't fun anymore. I gotta think about this
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
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 turningoff guy was right before them is too low.
 one year ago

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

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

MikaelBest ResponseYou've already chosen the best response.5
Welcome to our humble abode Mrs @sauravshakya @hartnn and all !
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.0
ACTUALLY THIS SIMILAR PROBLEM WAS ALREADY SOLVED BY ME TOO.
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.0
http://mathriddles.williams.edu/?p=146
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.0
THAT IS THE SIMILAR QUESTION....... only number are different..AND ITS LOGICAL NO SERIES
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.0
AS far as I remember.
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
ya, i have also seen such problems...
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
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
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
Because I have met this situation in real life engineering problem.
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
Thanks Highlander ....!
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
Best of luck. and keep them cool and well nutritioned !
 one year ago

siddhantsharanBest ResponseYou've already chosen the best response.0
Haha. Yeahh. Thanks. Nice problem though.
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
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.
 one year ago

MikaelBest ResponseYou've already chosen the best response.5
It is assumed the do communicate and agree beforehand.
 one year ago
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