OK everyone, since Genius decided to give us a puzzle, thought I'd give you one of my
own....
So if you've heard this one before, don't speak up, and if you haven't, think about it, don't
use the internet to get the answer, that's no fun now is it...;-)
Alright - you're in a waiting room with 99 other people, to make 100 in total. You're all told
that once you go into the next room, you'll be placed in single file line facing forward, such
that the guy at the back can see everyone in front of him, and the guy at the front of the line
can see no-one. Got that?
Once you're in this second room, you each get a hat put on your head, which is either black
or white. You can NOT see your own hat, but you can see the hat colour of everyone in front
of you, and not behind. (So, the guy in the middle of the line can see the hats of the 49 in
front of him, but not the 50 behind him.)
Once the hats have been placed on the heads, a guy with a gun goes to the back of the line
and points it to the head of the last guy in the line. The person can say either black or white,
and if they get their own hat colour correct, they survive, if not, they die. The person cannot
say anything else except black or white, just ONE word, and they have to get their own hat
colour correct to live. Once the outcome of that happens, the man with the gun goes to the
next person in line, and so on, until he reaches the front of the line.
OK, here is the question, what strategy can you come up with in the waiting room that will
save the most number of people GUARANTEED??
I'll give you a hint, you can save 99 of the people guaranteed....
Enjoy,
Joe
The person in the very back answers according to the rule:
when questioned, give the color of the hat directly in front of you.
The nest person will thus know the color of their own hat. They, in
turn will answer according to these rules:
If the person directly in front of you has a hat color corresponding to
the answer of the person in back of you, then repeat the answer.
If their hat is a different color answer as before only shout the answer
loudly.
If the person in back of you shouts their answer, then answer with the
hat color opposite the one they just gave.
can I have a shot? the last one is in danger : 50% chance.
He doesn't know , so for him, both colors are equally good.
They agree in the waiting room that he will call 'white' if he sees an
even number of whites in front of him. Regardless of what happens
to him, the others can make the sustraction. Theys just call their
color, making the even/odd count right with what they heard and see,
and their own.
Is that about right? sin
I've seen this problem before, and it was referred to as the "Saddam Hussein problem".
where Saddam had buried 100 POWs up to their necks in sand, so that they couldn't turn
around. The solution is exactly the one you just said. But... what happens if someone makes
a mistake? How many can you save then?