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A Riddle: Four Dudes in the Sand

Four teammates in a Survivor-esque reality TV show are competing for instant celebrity and $1,000,000,000,000,000,000,000,000,000,000. At the moment, they are buried in the sand, up to their necks.

One of them is buried on one side of a brick wall, and the other three are buried on the other side of the wall. All of them are facing the wall, and none of them can turn his head. The host of the show has painted X's on the backs of their heads — white X's on teammates 1 and 3, and black X's on teammates 2 and 4.

Because teammate 4 is buried behind teammates 3 and 2, teammate 4 can see the white X on teammate 3, and he can see the black X on teammate 2. Because he's buried behind teammate 2, teammate 3 can see the black X on teammate 2. Because he's buried in front of teammates 3 and 4 and facing the wall, teammate 2 cannot see any X's on anybody. Teammate 1 obviously cannot see any X's on anybody. None of the teammates has any way of seeing his own X or gaining any information about the color of his X from shadows, reflections in the TV cameras, paint spilled on the ground, etc.

The host tells the teammates that they will be eliminated in an hour unless one of them can figure out the color of his own X. Each teammate knows that there are four teammates total, and each teammate is told that two of them have a white X and two of them have a black X. Each teammate therefore knows that his own X is either black or white, but none of them knows which it is.

So, here is what each teammate knows:

Teammate 4: I have either a black or a white X on my head, as do the other teammates. Teammate 2 has a black X on his head, and teammate 3 has a white X on his head.

Teammate 3: I have either a black or a white X on my head, as do the other teammates. Teammate 2 has a black X on his head.

Teammate 2: I have either a black or a white X on my head, as do the other teammates.

Teammate 1: I have either a black or a white X on my head, as do the other teammates.

The team will be given exactly one chance to speak. The first teammate to make a noise must immediately state the color of his own X and explain exactly how he knows what color his X is. If he is wrong about the color of his X, the team will be eliminated. If he says anything that doesn't explain how he knows what color it is, the team will be eliminated. If his explanation gives the host the impression that he was guessing about the color of his X and got lucky, the team will be eliminated. If all of the teammates remain silent for the full hour, the team will be eliminated.

One of the teammates does figure out the color of the X painted on the back of his head and he is able to give the host a satisfactory explanation for how he knows.

Which teammate figures it out, and what is his explanation?

I will comment on this riddle in part two. Think about it, but do not post any comments in the Coffee Shop. If you try, the Editors will thwart you!