13 - TELL THE COLOR OF THE CAP:

100 Jews are caught by deadly Nazis. The Jews are asked to stand in a queue and they are marked with numbers from J1 to J100. And then the Nazis put on a cap on each of the Jews head. The caps are either red or blue and these are randomly chosen, ie. all the caps could be reds, or all could be blues, or 99 reds and 1 blue, or any combination is possible. In this scenario, the last person (J100) can see all the caps of the persons in front of him (J99 to J1), again J99 can see J98 to J1, ie. any Jew can see only the caps of the Jews standing in front of him. Obviously nobody can see his own cap and thus, the first person (J1) could not see any cap. Now, Hitler comes and asks each of the Jews, starting from J100, to tell the color of his own cap-- if he says it correct he will be freed, else killed. The intelligent Jews used a strategy such that at least 99 out of 100 could be saved surely. What was the strategy ?

13-Ans- J100 has no way of knowing the color of his own cap, but he can save other 99 people's lives.

J100 counts the number of red caps he sees in front of him, and if the number is EVEN he says "My cap is red", otherwise says "My cap is blue", without knowing what actually his cap is. Thus J100 has a 50% chance of survival, but people from J99 to J1 will definitely survive, as each of them hears what the previous person has said and knows what is the number of red and blue caps in front him.

The below figure describes the logic for 4 persons, the same logic will save any number of people: