top button
Flag Notify
    Connect to us
      Site Registration

Site Registration

How many prisoners can be saved at most?

0 votes
236 views

100 prisoners in jail are standing in a queue facing in one direction. Each prisoner is wearing a hat of color either black or red. A prisoner can see hats of all prisoners in front of him in the queue, but cannot see his hat and hats of prisoners standing behind him.
The jailer is going to ask color of each prisoner’s hat starting from the last prisoner in queue. If a prisoner tells the correct color, then is saved, otherwise executed. How many prisoners can be saved at most if they are allowed to discuss a strategy before the jailer starts asking colors of their hats.

posted Jul 29, 2017 by Biswajit Maity

Share this puzzle
Facebook Share Button Twitter Share Button LinkedIn Share Button

2 Answers

0 votes

99 prisoners can be saved and last prisoner will be executed as no one can see his hat

answer Jul 29, 2017 by Pratyush Pathak
0 votes

Answer:
At-most 99 prisoners can be saved and the 100th prisoner has 50-50 chances of being executed.
The idea is that every prisoner counts number of red hats in front of him.

100th prisoner says red if the number of red hats is even. He may or may not be saved, but he coneys enough information to save 99th prisoner.

The 99’th prisoner decides his answer on the basis of answer of 100’th prisoner’s answer. There are following possibilities and 99’th prisoner can figure out color of his hat in every case.

If 100’th prisoner said ‘Red’ (There must have been even number of red hats in front of him)
a) If 99’th prisoner sees even number of red hats in front of him, then his color is black.
b) If 99’th prisoner sees odd number of red hats in front of him, then his color is red.

If 100’th prisoner said ‘Black’ (There must have been odd number of red hats in front of him)
a) If 99’th prisoner sees even number of red hats in front of him, then his color is Red.
b) If 99’th prisoner sees odd number of red hats in front of him, then his color is Black.

The 98’th prisoner decides his answer on the basis of answer of 99’th prisoner’s answer and uses same logic.

Similarly other prisoners from 97 to 1 are saved

answer Sep 21, 2017 by Mogadala Ramana



Similar Puzzles
+1 vote

Anya is a clever trader of rare artifacts. Each day she carries three boxes with each filled with thirty artifacts. The boxes cant hold more than that. She travels far of northern lands to sell these artifacts but on way, she comes across thirty checkpoints where she has to shed one of the artifact for each sack to the authorities for letting her pass.

How many artifacts will be left with her when she reaches her destination crossing all the check points ?

+1 vote

Rohan is on his way to visit his girlfriend, who lives at the end of the state.It's her birthday, and he want to give her the cakes that he has made.Between his place and her girlfriend's house, he need to cross 7 toll bridges.
Before you can cross the toll bridge, you need to give them half of the cakes you are carrying, but as they are kind trolls, they each give you back a single cake.

How many cakes do Rohan have to carry with him so he can reach his girlfriend's home with exactly 2 cakes?

+5 votes

A light bulb is hanging in a room. Outside of the room, there are three switches, of which only one is connected to the lamp. In the starting situation, all switches are 'off' and the bulb is not lit.If it is allowed to check in the room only once to see if the bulb is lit or not (this is not visible from the outside), how can you determine with which of the three switches the light bulb can be switched on?

0 votes

Starting with any number at all, I can always reduce it to 4 by applying a consistent rule. 4 is the magic number.
Example: 100. 100 is 10, 10 is 3, 3 is 5, 5 is 4, and 4 is the magic number.
Another Example: 52. 52 is 8, 8 is 5, 5 is 4, 4 is the magic number.
Find out what is the rule?

+1 vote

If Kareem Khan is standing in a row of prisoners at 9th position from both end of a line. How many Prisoners are standing in total ?

...