conundrum #2

Conundrum #2
Four trawlers were hijacked by Somali pirates. Their captains were taken to desert island, where they were to be shot. When they arrived at the island, a discussion amongnst the pirates ensued. How should they be shot? And, shouldn't they be tortured first? They came up with a plan. The captains were buried in the sand up to their necks. The first captain was buried facing a wall, he could see the wall and nothing else. The second captain was buried facing the other side of the wall, he could see the wall and nothing else. The third captain was buried behind the second captain. He could see captain #2 and the wall and nothing else. The fourth captain was buried behind the third captain. He could see captain #3 and captain #2 and the wall and nothing else. In an unlikely gesture of humanity, the Somali's provided each captain a hat to ward off the sun. The captains were told that the four hats provided were 2 red hats and 2 black hats. The captains could not see the color of the hat they were wearing. However, captain 4 could see the hats on captain 3 & 2, and captain 3 could see captain 2's hat. Captain 2 and captain 1 could only see the damn wall.
The captains were told that they would undergo an intelligence test before being shot. They were told they would be given 5 minutes to ponder their answer, but if they spoke to each other they would be shot. At the end of 5 minutes, one of the captains must say what color his hat is. If he is wrong they will all be killed. If he is right, they will be deemed smarter than the average trawlerman and allowed to return back to their boats alive.
At the end of 5 minutes, one captain speaks up. Did they live? which captain spoke up? Why was he certain of the color of his hat?

Greetings,
#3 spoke up and said my hat is the opposite color of #1's and they all sang as they went back to the boat...

Men Without Hats - Safety Dance [Official Video] - YouTube

You meant #4 spoke up, not #3, right?

Greetings,
Mr.Marin. Thank you. Yes I meant to say #4 spoke up.

So red is the opposite of black? Hummm -------. How does opposite translate into Somali? Too many unknowns for logic 101 to apply. Just shoot me.

Greetings,
OK, opposite wasn't the best word maybe. #4 could have asked the pirates what color #1's hat was and picked the "opposite" color or if #3 was bald, #4 could have pulled #3's hat off with his teeth and seen the color of his own hat in #3's sweaty bald head for they surely would have been sweating given their predicament and being on a desert island and all. How about aliens? Ya, that's it. Aliens saved 'em all.

Ya'all are making this too hard. RTF came close, and the video was a classic, but alas, no cigar. This is really pretty easy, the answer is obvious after you hear it, but perhaps not until. Let's give this another day and see if we can drum up a few more ideas. There are no tricks to the answer, no aliens either.

The answer

THE ANSWER

RTFirefly had it, I thought when I first read his response. I was obviously swayed by his cool video. But on second reading, he got the right captain but wrong color. He said "# 3 spoke up and said my hat is the opposite color of #1's". #1's hat is black. I suspect he meant to say my hat is oposite color of #2's. #2's hat is red. That would have been correct since the 'opposite of red is black' in ths example. No cigar, well, maybe at least a half cigar for the video.

In the end the Captains survived. At the end of five minutes captain # 3 spoke up and said 'My hat is Black'. How did he know?

The answer to Conundrum #2 is as follows:

All four captains had been told that there are two black caps and two red caps, but none knows which color hat has been placed on his own head.

Captain #3 waited until close to the end of the allotted 5 minute time period waiting to hear if Captain #4 would speak up. Captain #3 knew that if Captain #4 saw two hats of the same color in front of him on Captains # 2 and #3, he would have known that he was wearing the cap that was not the same color as theirs. Since Captain #4 didn't speak up, #3 reasoned that he (#3) could not be wearing the same color cap as the Captain (#2); therefore, his own cap must be black.

Very clever. Actually, RTF's answer was also correct because while he typed #3 in his solution he meant to say #4 as he explained later. At least his answer is correct if you accept the statement "My hat is the opposite color (or other color) than #1's" in lieu of naming the actual color. From their reputation of not being the sharpest tacks in the box, the Somali pirates would probably have become so confused at that point that they would have begun arguing over the meaning of "opposite" and eventually shot each other.

After waiting a minute or so, # 3 spoke up. Assuming all the trawlermen were similarly intelligent, he knew that if #4 saw two hats alike on #3 and #2, #4 would have spoken up immediately, knowing that he and #1 would've had the same (opposite color) hats. . Therefore, he knew that since #2 had a red hat, his must be black. Therefore #4 had to have a red hat, #3 had to have a black ahat, and #1 had to have the other black hat.