100 prisoners and the Light Bulb Puzzle

1,285.7K Views

There are 100 prisoners are in solitary cells, unable to see, speak or communicate in any way with each other. There’s a room with one light bulb, the bulb is initially off. No prisoner can see the light bulb from his own cell. Everyday, the warden picks a prisoner at random, and that prisoner goes to the that room. While there, the prisoner can toggle the bulb if he wishes. Also, the prisoner has the option of asserting the claim that all 100 prisoners have been to the living room. If this assertion is false (that is, some prisoners still haven’t been to the living room), all 100 prisoners will be shot for their stupidity. However, if it is indeed true, all prisoners are set free. Thus, the assertion should only be made if the prisoner is 100% certain of its validity.
Before the random picking begins.All the prisoners are allowed to get together to discuss a plan.
Note that each prisoner can be selected any number of times and the process will continue till the assertion is not made.

anikam Expert Asked on 22nd August 2015 in

The prisoners need a way to communicate with each other on who when into the cell. Therefore one person is chosen as the counter.
Every time any prisoner is selected other than counter person , they follow these steps. If they have never turned on the light bulb before and the light bulb is off, they turn it on. If not, they don’t do anything.Now if Counter person is selected and the light bulb is already on, he adds one to his count and turns off the bulb. If the bulb is off, he just sits and do nothing. The day his count reaches 99, he calls the warden and tells him “Every prisoner has been in the special room at least once”.

pnikam Expert Answered on 22nd August 2015.
```The prisoners give themselves numbers from 1 to 100 and determine among themselves what each prisoner should do when he leaves.
Every prisoner whose number is less than 100 turns on the lamp if it is off and on the condition that he has never turned it on yet.
The prisoner whose number is 100 turns off the lamp if it is on and counts the number of times he turned it off.
After counting 99 times, he informs the warden that all prisoners have already gone out into the room at least once.```
Moshe Expert Answered on 15th January 2023.

• More puzzles to try-

• Serial Vowels riddle

The word FACETIOUSLY contains the six vowels, A-E-I-O-U and Y, in their alphabetical order. Find another English word that does ...Read More »
• Cause me to smile

A time when they are green, a time when they are brown, but both of these times, cause me to ...Read More »
• Puzzlefry Marathon Riddle

The recent Puzzle fry annual marathon has just taken place. The judges have given up keeping a track of who ...Read More »
• Spy under blanket

What do you call a spy who sleeps with a blanket over his head?Read More »
• No direction place

Where is no direction like south, west, nor east, and weather not fit for man or beastRead More »
• Face the Word

Identify The phrase in the picture.Read More »
• Fortune Teller predition puzzle

There is a village that has five fortune tellers. The first fortune teller’s prediction has 83% chance of being correct. ...Read More »
• Very Exciting

It is very interesting and knowledgeable. Its front is very eye catching but its inside tells all. What is it?Read More »

You are invited in a party with some gifts. Only certain things have to bring through. You can bring a ...Read More »
• Not for reading or writing

Which type of paper can not be used whether for reading or for writing ?Read More »

There are 5 squares in this image. By moving only 2 matchsticks make seven squares. (Overlapping or breaking of matchsticks ...Read More »
• Measure exactly 4 cups of sugar

You are in a cookie factory, and need to make a huge batch of chocolate chip cookies. The recipe calls ...Read More »
• Three number series puzzle

Can you find the next three numbers in the given series? 4, 6, 12, 18, 30, 42, 60, 72, 102, ...Read More »
• Dodge ball game strategy puzzle

You, Andrew and Steve decided to play a game of dodge ball. You’re all will be standing in a triangle ...Read More »
• Chains Puzzle

You have five pieces of chain, each consisting of three links. You want to make one long chain of these ...Read More »
• Falling Trees

At my glorious call, the tallest trees fall, Some may resist, but only for so long. What am I?Read More »
• The things I bite, do not bleed

The things I bite, do not bleed, I do not bite until you push me; I bring my victims together ...Read More »