Prison Break tactic riddle
Prison guards are bored so during dinner they announce the prisoners that they will play a game:
In the morning they will stand in a line so that every prisoner will see all standing in front of him but no one behind him. Guards will randomly paint red or white stripe on their back. They will ask prisoners one by one from the last to the first. They will be allowed to say just one word “red” or “white”. If the prisoner says the color he has on his back he may go home in opposite case he will be executed without delay.
The prisoners are in one cell during the night and they can discuss the tactics.
What is the best tactic? How many will survive?
Prisoners decide and assign a colour to indicated Odd or even number of red striped prisoners visible to rear most prisoner.
e.g.
Red for even no.of red strips
White for odd no. of strips.
This will give probability of saving all except the rear most, and 50% probability for rear most prisoner.
Explaination:
Assume 10 prisoners with 1 R W R R W R W W R W 10th.
Now Prison guard asks 1, and 1 can see 4 R’s even no., so he says Red.
Now No. 2, knows that 1 could see even no of red, and he is also seeing 4 R’s even, so his color must be white. He says white, saved.
Now No. 3, knows that initially there were even no. of red, and he can see 3 Rs, no prisoner behind him has said red, so his own color should be red. Says Red saved.
Now No. 4, Initially even no of red, 1 red gone, there should be odd no. of Rs, but he can see only 2Rs, so his own color shoul be R. says Red saved.
Now No. 5, Initially even, 2Rs gone, should and can see even no. of R, so, his color is white.
Now No 6, Initially even, 2Rs gone, he can see odd so his color is Red.
No 7, Initially even, 3Rs gone, he can see 1R so his color should be white.
No 8, Initially even, 3Rs gone, he sees 1R, so white is the colour.
no 9, Initially even, 3Rs gone, he sees no R, so his color is Red.
no 10, Initially even, 4Rs gone so his color should be white. and saved.
If prosoner 1 color has been white he would die rest are saved.
Since there are 99 people that the last one sees, then
1) equality between the number of white and red is not possible
2) one of the groups is odd.
He will count how many there are in each group and say the color of the odd group.
The next one after him will count the stripes in front of him and if he sees an equal number of the same color as the first
said then it is his color otherwise it is the other color.
(Starting with the second prisoner, everyone sees how many are in front of them and know how many left before them,
and what the first one said (meaning which group is the even)) and so they can, in the worst case,
reach a score of 99, because only the person in the rear is guessing.
Your Answer
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