Tuesday puzzle

Re: Tuesday puzzle

When you choose your spot in line, make sure that all the red hats are on one side and the green ones are on the other.

But if

you can't communicate in any way and you don't know what color you have on which side do you line up on? Could they talk before going out? If so, Bill could be right. If no communication before going out and if no pre arranged signal as to what color the newly arriving person has on there is no way to line up. Once in line if they talked beforehand, it is possible except for the last person who gets a 50/50 chance if the red and blue hats are not equal.

Re: But if

No talking beforehand or other form of communication. Also, the exact number of people or ratio of hats is unknown by anyone.

It is solvable ;-)

Is seeing communication?

Person 1 goes out he is wearing red or green. Person two goes out he is wearing red or green so he stands beside the other. The third person goes out and he stands between the two. Now we have two red or two greens or three of each. At this point all is correct and cannot be wrong. The fourth person goes out and stands between the center two. If the hat he is wearing is the same the two others with the same color have they stay where they are. If he goes between colors that are different the people already in place who can see the different colors move so that they insert themselves within the same color. If the persons are of the same color now then all is correct. If the new placement makes the colors different the people on either side of the new person move to thier former side person so that they are beside the inside person they started with. This way the colors sort themselves by forcing the odd color to one side or another moving away from the original two. It gets to be like a chinese fire drill, but the odd man out keeps being forced out the side. The color doesn�t matter only that they are the same or different. The ratio doesn�t matter because all depends on the side you are on and what is seen beside you and if the others on the sides of you move or not. Of course they could be all red or green, or only one of one color and all the rest the other but the problem said about 50/50.

Re: Is seeing communication?

Once they go out, they can move side to side, but cannot switch places.

Re: Is seeing communication?

One goes out--red or green

Two goes out--red or green--#one sees #two

Three goes out--red or green therefore there are two of one or three of one. To give him the correct place they stand aside to let him in.

There are now two of one color or three of one color.

Four goes out and he can see the others and they see him. As he walks toward one side or the other, they either close ranks or open up. Now it is apparent to all four which side is red and which is green. with only 25% chance all red or all green. No matter, as each other person comes out the sides open or shift as to the color that person is wearing. When ten people are out they are divided as to color in whatever ratio there is.

Re: Is seeing communication?

It is simpler than you think. Nobody ever needs to know what color their hat is (although some will figure it out eventually). Each person simply finds a place in line where all greens are to one side and all reds are on the other.

If the line is all green or all red, either end will do.

If the line is part green and part red, there will be only one location that satisfies the constraint (assuming everyone else has followed the same rule.)

Re: Tuesday puzzle

They all remove their hats and place them on the ground in a line. All green to one side and all red to the other. They all line up behind the hats and place them back on their heads.

Tom

;-)

That is it. Gary sorta had it except that moving aside would be a form of communication. The person going out just has to place him/herself in the spot between the two colors, wherever that is.