Escape the Aliens!
Aliens have took 10 people from Earth to see if humans are smart enough to live. The aliens give you a few hours time to discuss a strategy to solve this challenge:
Each of the 10 people will be placed in a line, tallest to shortest. Each person will get a hat, either red or blue, and will not be able to see their hat. The person in the back can see everyone's hat color, the person in the front can't see anyone's hat. The aliens will ask each person what their hat color is, starting from the back, and will continue forward. If at least 9 people get their their hat color right, humans will be spared. Talking to each other and using and symbols are not allowed. You can only say "Blue" or "Red".
Given that every person knows these instructions and uses optimal play, Is it possible to save humanity?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Yes it is possible.
Here is the strategy:
The first person in line will say "Red" if they see an odd amount of red hats in front of them, and "Blue" if they see an even amount of red hats in front of them.
The second person in line will see some hats in front of them. Lets assume the first person saw an odd amount of red hats. If the second person sees an odd amount of red hats, then they know their hat is blue, as the first person also saw an odd amount of red hats. But if they saw an even amount of red hats in front of them, they know that there hat is red, as the first person saw an odd amount and the second person sees an even amount, the only difference is the second persons hat. Lets say that the second person saw an even amount of red hats in front of hit, and thus, said "Blue".
The third person will know that the second person saw an even amount of red hats in front of him, because he will be imagining that he was the second person and saw an even amount of reds, because if he saw an odd amount, he would have said "Blue". So now he will do the same thing person two did to figure out what hat color he has.
Everyone else will repeat this process to find everyone's hat color. The first person may of may not get his hat color correct, but everyone else will as long as they play optimally.
So yes, they can save Earth and the rest of humanity.