[sgbuffett]

It's not a trick question that plays with words.


Rules and puzzle clearly stated below.



In this problem, 100 numbered prisoners enter a room to find their own numbers one by one . Their number is hidden in one of 100 boxes. In order to survive all prisoners have to find their number and
if  anyone cannot all will die . The rules state that each prisoner may open only 50 boxes and cannot communicate with other prisoners. They have to leave the boxes as they are before they entered the room. The prisoners can only  strategise before it starts on what to do. So what is the best strategy?

At first glance the chance of prisoner surviving is 0.5^100 since each prisoner only has 0.5 chance of finding his own number.

There is way to do it that gives a probability of around 30%. The solution is fascinating.

[WhatDoYouThink?]

if each randimly chooses the boxes, his max average survival rate is 50/100 = 50%

but for the entire group of 100 to do that and all survive, the probability is 0.5^100 which is almost 0.

they can try using the cycle following method which gives much higher chance than 0

[Blin]

if i found my number can i leave it open out side the boxes for bros to see?.

[Sentinel]

Monty Hall puzzle lah

knn

[sgbuffett]

if i found my number can i leave it open out side the boxes for bros to see?.

No you have to leave the room and boxes exactly the same as when you enter the room..all boxes have to be closed after you look for your number.

[Blin]

No you have to leave the room and boxes exactly the same as when you enter the room..all boxes have to be closed after you look for your number.

 like that all mati case unless prisoners do a break out .

[sgbuffett]

 like that all mati case unless prisoners do a break out .

There is a genuine solution that gives 30%  chance of survival.

To appreciate the solution one has to try to solve the puzzle first to understand the difficulty

[WhatDoYouThink?]

could be this modified cycle following algorithm:

if your number is x, open box(x), if box(x) = x, then you stop and stay alive. else open box(box(x)), and repeat the cycle.

[sgbuffett]

could be this modified cycle following algorithm:

if your number is x, open box(x), if box(x) = x, then you stop and stay alive. else open box(box(x)), and repeat the cycle.

Very impressive if you thought of this independently. 

I did not come close...because it is not apparent it will give a better probability of survival on first look

[WhatDoYouThink?]

Very impressive if you thought of this independently. 

I did not come close...because it is not apparent it will give a better probability of survival on first look

aiya quite common when doing memory search.

if by random search, you hv to keep track of those numbers searched, so as not to waste your search time and reduce yr chances of survival. if the database is huge, then the overhead is substantial. 

using cycle following the overhead is reduced substantially, but still hv to remember the starting number of each cycle.

by modifying the cycle following method, you only need to do 1 cycle, and there's no overhead at all

[Sentinel]

Already said Monty Hall puzzle

Is this so difficult to digest?

[sgbuffett]

Already said Monty Hall puzzle

Is this so difficult to digest?

This is not the Monty Hall puzzle lah. In Monty hall contestant is to choose one of 3 doors behind which is a prize behind one door.
The contestant choose one door  then the host opens one door that is empty and ask him if he wants to switch. The correct answer is always switch.

I could solve Monty Hall quite easily when it came out either using logic or conditional probabilities.

This prisoner  puzzle I could not solve. The answer is unexpected.

[p1acebo]

The answer is to strip naked and get bukkake by the guards to survive

[sgbuffett]

Here is a full explanation of the puzzle and solution.

A research paper by a computer scientist with the algorithm was published a few yrs ago. The solution can be extended to infinite number of prisoners. 10M prisoners will also have 30% chance to survive using the strategy.

Watch and enjoy.

[Sentinel]

This is not the Monty Hall puzzle lah. In Monty hall contestant is to choose one of 3 doors behind which is a prize behind one door.
The contestant choose one door  then the host opens one door that is empty and ask him if he wants to switch. The correct answer is always switch.

I could solve Monty Hall quite easily when it came out either using logic or conditional probabilities.

This prisoner  puzzle I could not solve. The answer is unexpected.

Same lah

Both are counter-intuitive but the mathematical logic is the same

The probability is altered by info obtained inherent in the situation

The Monty Hall puzzle, the opening of one door to reveal what is inside changes the probability

The Prisoners puzzle, linking the prisoner number to the box number form a chain that is finite by the number of boxes, thus changing the probability

[WhatDoYouThink?]

if you start with a random number, you may hv to find your own number in multiple loops.

but if you start with yr own number, you'll definitely find yr own number in a single loop

[Sentinel]

If I can solve this puzzle with a strategy that guarantees the 100 prisoners will live every time, then I've reached ascension completely

[Sentinel]

The fact of the matter is that God does not play dice, so probability is a manifest of lower dimensions of existence

At a much higher plane, nothing happens by chance

Case closed

[kc172021]

No you have to leave the room and boxes exactly the same as when you enter the room..all boxes have to be closed after you look for your number.

just place the correct number to the correct box , then the next should do the same. the Problem is what if the first one cannot
find his own correct number. then game over for the rest of 99. likewise for the subsequents

[Blasterlord2]

The fact of the matter is that God does not play dice, so probability is a manifest of lower dimensions of existence

At a much higher plane, nothing happens by chance

Case closed

I don't believe in god creating this world but yes, in Buddhism it's the same - nothing happens by chance.

Anyway, this is just a fun riddle, no need to involve the 'higher plane' 

[RichDad]

In the end, sadly the prisoners only have a 30% of surviving using the loop strategy.

70% probability die.

Tang See?

[WhatDoYouThink?]

for an individual prisoner, his chance of survival is 50% no matter what strategy he uses.

for the entire group to survive together, the chances are almost zero. if they follow the cycle following method, the survival rate increases to 30%

[WhatDoYouThink?]

actually the maths behind this puzzle is rather straightforward. let me try to work it out.

as long as a cycle length is > 50, the whole group will die. so the probability for the entire group to die is simply:

1/51 + 1/52 + .... 1/100
= H100 - H50

use a scientific calculator to find the harmonic numbers:

= 5.18738 - 4.49921
= 0.68817

so the group survival rate is 1 - 0.68817 = 31% QED

[RichDad]

actually the maths behind this puzzle is rather straightforward. let me try to work it out.

as long as a cycle length is > 50, the whole group will die. so the probability for the entire group to die is simply:

1/51 + 1/52 + .... 1/100
= H100 - H50

use a scientific calculator to find the harmonic numbers:

= 5.18738 - 4.49921
= 0.68817

so the group survival rate is 1 - 0.68817 = 31% QED

Correct. About 30% survival rate. But if they don't use this strategy, it is much much lower.

It is just a silly problem thst won't happen in real life anyway.