One hundred prisoners are given the chance to be set free tomorrow. They are all

Question

One hundred prisoners are given the chance to be set free tomorrow. They are all told that each will be given a red or blue hat to wear. Each prisoner can see everyone else’s hat but not his own. The hat colors are assigned randomly and once the hats are placed on top of each prisoner’s head they cannot communicate with one another in any form, or else they are immediately executed. The prisoners will be called out in random order and the prisoner called out will guess the color of his hat. Each prisoner declares the color of his hat so that everyone else can hear it. If a prisoner guesses correctly the color of his hat, he is set free immediately; otherwise he is executed. They are given the night to come up with a strategy among themselves to save as many prisoners as possible. What is the best strategy they can adopt and how many prisoners can they guarantee to save? Explain your answer.

Explanation / Answer

Solution :-

The best available startegy in this scenarios is explained by using simple rule of even and odd

and we can use the following steps to save most number of inmates

Conditions :-

1. A prisoner can see a total of 99 hats

2. Total number of Blue and Red hats are not given

3. But he will either see a total even number of blue hats or even number of blue hats (vice versa for red hats)

The Prisoner shall amongst themselves decide the whosever goes first shall communicate the Color of Even Hats (or it can also be odd but we will use Even in this strategy ) he sees .and the rest of all the inmates will get check weather there are even or odd hats excluding the color of their hat and they shall know what color is their hat .

Lets See if the strategy shall work or not:-

* The prisoners were given 40 Red and 60 Blue hats

* The First person who is called is wearing a Red Hat and sees Odd Red and Even Blue Hats

* The Person Calls the color Blue Being decided amonngst themselves to shout even color

* If the person is wrong and shot immediately that would mean there were actually odd number of that color

and if he is not shot that means that there were actually even hats of that color

* The one Wearing the red hat will also see even blue hats which means they did not missed theirs and are definetly wearing a red one (vice versa if he is shot)

* The Person Wearing Blue hat will see odd number of blue colored hats and they will immidiately know they are missing their own in counting even hats and they shall also know their color of hat (vice versa if he is shot)

* The first person has also a 50 % chances of calling the right color but we can gurantee to save the rest 99 Inmates by being able to know the even and odd numbers

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