Puzzle 18

Welcome back! Let’s go straight to the puzzle.

A king in medieval times thought his seers were giving him wrong information. Like when they said they foresaw a expansion in the empire, but a savage horde conquered half his kingdom the next day. So he had a idea. He went to a hat-maker and had him make a random number of red and blue hats. The hat-maker complied and made a random number of red and blue hats.

The king then tells his 100 seers he is about to line them up and that he will place either a red or blue hat on each of their heads. Once lined up, they must not communicate amongst themselves. Nor may they attempt to look behind them or remove their own hat.

The king tells the seers that they will be able to see all the hats in front of them. They will not be able to see the color of their own hat or the hats behind them, although they will be able to hear the answers from all those behind them.

The king will then start with the seers in the back and ask “what color is your hat?” The seers will only be allowed to answer “red” or “blue,” nothing more. If wrong then they will be killed

The king will then move on to the next seer and repeat the question.

The king makes it clear that if anyone breaks the rules then all the seer will die, then allows the seers to consult before lining them up. The king listens in while the seers consult each other to make sure they don’t devise a plan to cheat. To communicate anything more than their guess of red or blue by coughing or shuffling would be breaking the rules.

What is the maximum number of seersĀ  they can be guaranteed to save? Because, of course, they are all frauds.

Random guessing guarantees saving 0 of them so keep that in mind.

If you think you know the answer comment below. I’ll put the answers in the comments in one week. Have fun!

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One Response to Puzzle 18

  1. James says:

    99 and a 50/50 chance to save 100
    How? you ask?
    So how can 99 people be saved? The first wise man counts all the red hats he can see (Q) and then answers “blue” if the number is odd or “red” if the number is even. Each subsequent wise man keeps track of the number of red hats known to have been saved from behind (X), and counts the number of red hats in front (Y).

    If Q was even, and if X&Y are either both even or are both odd, then the wise man would answer blue. Otherwise the wise man would answer red.

    If Q was odd, and if X&Y are either both even or are both odd, then the wise man would answer red. Otherwise the wise man would answer blue.

    If you don’t understand Go here it’s puzzle #2 I can’t believe that is the only site that explains it so.

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