SOLUTION: Minimum of 19 members can be saved
First guy needs to sacrifice himself (Whether he lives or not depends on his luck).
The sole duty of the last person (to whom the question is asked 1st) needs to establish
the parity of the BLACK hats.
If there are even number of BLACK hats, he says BLACK, else he says RED.
(If his answer suits his hat colour, he lives. If not he dies).
Now the duty of the 2nd last person is to observe the parity of the BLACK hats.
If he finds even number of BLACK hats,it means that his hat colour is RED.
So he says RED & he lives.
Now, the 3rd last person needs to work a bit more hard.
He need to remember the previous 2 answers and analyse his hat.
As the last person said BLACK, it means there are even no. of BLACK hats at that stage.
As the 2nd last person said RED, it means that the no. of BLACK hats is still even.
If he finds odd no.of BLACK hats, his hat colour must be BLACK, else RED.
This procedure is followed by the remaining people till the 1st person. Thus the complexity
increases and hence they need to place themselves such that most intelligent person in 1st
place in the queue and the least intelligent person in the last place in the queue.
Thus a minimum of 19 members can be saved and if luck favours all of them can be saved.
the parity of the BLACK hats.
If there are even number of BLACK hats, he says BLACK, else he says RED.
(If his answer suits his hat colour, he lives. If not he dies).
Now the duty of the 2nd last person is to observe the parity of the BLACK hats.
If he finds even number of BLACK hats,it means that his hat colour is RED.
So he says RED & he lives.
Now, the 3rd last person needs to work a bit more hard.
He need to remember the previous 2 answers and analyse his hat.
As the last person said BLACK, it means there are even no. of BLACK hats at that stage.
As the 2nd last person said RED, it means that the no. of BLACK hats is still even.
If he finds odd no.of BLACK hats, his hat colour must be BLACK, else RED.
This procedure is followed by the remaining people till the 1st person. Thus the complexity
increases and hence they need to place themselves such that most intelligent person in 1st
place in the queue and the least intelligent person in the last place in the queue.
Thus a minimum of 19 members can be saved and if luck favours all of them can be saved.
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