I’m not so sure about this.
What if the words are something like “single” or “double”. They are measurments, which can be compared to each other in a definite way, but they themselves are not definite.
My coworker just nailed me with this one, and it’s the first logic-based (as opposed to “create a scenario” such as the albatross soup) puzzle that’s stumped me in a while. (Which probably says something about the difficulty, or lack thereof, of crap I’ve been hit with.)
This one’s a tad hard to explain - it’s more visual - but here goes.
Four people are buried up to their necks in a straight line, one behind the other. The first person is facing the other three, but between him and them is a wall that is opaque that is infinitely tall and infinitely long (read: you can’t see around, over, or through it). Each person has a hat that is either black or white. Nobody can see their own hat, and each person can see only those of the people in front of them. (All four people are facing the wall, by the way.)
So the fourth guy can see what hats #2 and 3 are wearing, #3 can see #2, and #2 can only see the wall. To be dug up, somebody needs to know, beyond a doubt, who is wearing which hats. They can not turn, or free themselves, do not speak, and there are no reflective surfaces anywhere.
For the record, person 1 is wearing black, two is white, three black, four white. So, if you were to draw it it would look like:
B | W B W
With everybody facing the wall.
The answer to this is self-evident once you get it. In other words, you won’t need to ask me if you’re correct (no digging out, no communication between the people, no reflective surfaces, passers by, or falling hats). The people knows the formation they’re buried in, and they all know there are two hats of each color. Beyond this, they, and you, are on their/your own. Good luck.
No scenes from the exorcist, meaning no heads spinning 180[sup]o[/sup] and no way to see behind oneself, peripheral vision be damned.
Second riddle: There are 5 barrels of apples. Four of the barrels contain apples that weight exactly one pound each. The fifth barrel contains apples that weigh 1.1 pound each. For all intents and purposes, this difference can not be discerned by looking, hefting, or eating the apples. On the other hand, there is a lady with an extremely shitty scale, who will let you use it to weigh whatever you want. The catch is that this scale will accurately weigh only one weight, at which point the needle gets stuck at that weight. Which means that you can only use it once. Adding or removing weight will not move the needle one bit.
So, without stooping to water displacement (it’s in the desert, okay?) or other means, figure out which barrel has the 1.1 pound apples.
KKB- are you sure you have not left something out?
Riddle 2 is fine, altho the “shitty” scale has to be real accurate- wieght 1 apple from bbl #1. 2 from bbl#2, etc., all at the same time. If the 1.1 lb apples are in #3, say, then it will be .3lb overwieght, if in bbl #1, then .1ln over, etc.
KKB- You must have left something out.
At this point, both Person #4 and Person #3 know the set-up of Person #2 and Person #3. Person #4 can see them, and Person #3 (seeing Person #2’s hat) knows that if his hat was white, Person #4 would know the full scenario (as both Person #2 and Person #3 would be wearing white hats, leaving Person #1 and Person #4 to have to be wearing black hats). Ergo, Person #4 (by sight) and Person #3 (by logic) know which hats are on Persons #2 and 3.
Unfortunately, that leaves a black hat on 4 and a white hat on 1. Or the other way around- can’t see the puzzle from the reply screen. But either way it’s the same situation- no one has any information on person #1 or 4 other than one is wearing a white hat and the other is wearing a black. But that’s it. So until someone can catch a glimpse of hat #4 or #1, there’s no way for any of them to get free.
Unless the ‘solution’ to the puzzle is, “And they all bake to death in the hot sun, which is just punishment for those who come up with these abosultely bizzarre and unrealistic scenarios.”
Thanks John, I was hoping I wasn’t crazy- or if i was, i had some company. 
If that wall was transparent, tho…
I’m going to take a stab at this.
I’m assuming this isn’t some sort of weird word-play problem or Greek riddle or something. That this is a real problem that can be solved through observation, logic and deduced or infered from new information. If a person were somehow ACTUALLY in this circumstance they could puzzle their way out of it.
Fair enough.
Okay, we’ve got 4 guys. None of them are supposed to communicate between each other. One guy is all by himself on the other side of an infinitely long and high opaque wall. Can’t see over, through, or around it. The guy all by himself ( Guy no.1) is wearing a black hat but doesn’t know it. The next guy on the other side of the wall (Guy no. 2) is wearing a white hat, but doesn’t know it, either. Guy no. 3 is wearing a black hat, can’t see his own hat, and can see the guy’s hat in front of him. The last guy is wearing a white hat, can’t see his own hat, and can see the hat of Guy no. 3 (black) and guy no. 2 (white).
B | W B W
Only one of these guys needs to know for sure who is wearing what for them all to be freed.
Well, the guy by himself on the other side of the wall is SOL. He can’t contribute to any knowledge about himself, let alone anyone else’s situation. He can only come up with the possible combinations of four guys wearing two white hats and two black hats. (6) Sucks to be that guy.
The second guy immediately on the other side of the wall isn’t much better off. Sure, he’s got company, but he doesn’t know which hat he’s wearing, let alone anyone else’s. He can’t do anything to find out about the other two guys behind him. Sucks to be him, too.
The third guy knows that the second guy is wearing a white hat. He must feel frustrated as hell, not knowing his own hat’s color and only guessing at the other guys’. Kinda sucks to be him, too.
Last guy, guy no. 4, has the most information at his disposal. He knows the colors of two hats with certainty. He knows that there are two black hats and two white hats involved in this scenario. If he can somehow determine the color of his own hat, he can by process of elimination determine the hat of the guy on the other side of the wall and get himself and these other guys out of this.
So.
I’m making one assumption about these hats that might not be true: that these hats are EXACTLY the SAME size and shape except for their color. But nothing in this puzzle has stated that explicitly. Suppose the white and black hats were different shapes and sizes? Suppose the white hats were chef’s hats and the black hats were top hats?
My first solution is easy: barring talking, digging his way out, trying to dislodge his hat, or looking around in vain for passersby and reflective surfaces, the last guy just looks at the shadows on the ground. He notes that the shadow of his hat matches guy no. 2’s shadow and screams “Okay! I’m wearing the WHITE hat, same as guy no. 2! The guy in front of me is wearing a black hat, same as the guy on the other side of the wall! Now get me the hell outta here!”
Okay. That works if the hats are different shapes. What if the hats were basically the same size and shape? A possible second solution that the white hats, unlike the wall, might be slightly transluscent, allowing a little sunlight to shine through them. Careful observation of the shadows might allow guy no, 4 to see this difference and still deduce the hat colors correctly.
Okay. Suppose they were EXACTLY the same hat except for color?
Hm. Well. I personally don’t wear black hats in the when its sunny much because that makes me sweat. Now if these guys were outside in the sun buried up to their necks and unable to move, I’d be willing to bet the guys in the white hats (no. 2 and no. 4) would be more comfortable than the black hat guy (no. 3). No. 4, noticing how guy in the black hat is getting cooked, deduces that his hat is white like no. 2.
I have a few more wild guesses based on how, using sensory information, guy no. 4 might determine his hat is white based on smell, touch and taste (Don’t ask). How’d I do? I hope I got this right because I wasted over half an hour on this…
Guy #4 sees black and white hats in front of him. He sees black hat #3 die of sunstroke so he deduces that he cannot be wearing a black hat. He therefore knows that he is wearing a white hat and therefore guy #1 is wearing a black hat.
He has the solution and they are all freed, except that guys #1 and #3 are dead already.
All hats are exactly the same except for color. The location is indoors (for some Godforsaken reason). All 4 participants are relatively clever individuals, with a decent grasp of logic. None are suicidal, and all want to leave as soon as possible. These wishes are known, and all four would know the instant somebody “won” (when that person calls the unreflective, unbiased, unresponsive referees).
So, again, who wins and how?
Seriously, you guys are really, really close.
Actually, never mind, either I or my coworker have been smoking the crack rock. There’s something wrong here - I’ll know on Monday what it is/was.
To make up for this fiasco, here’s one that I do know is correct.
There are two rooms down the hall from each other. One room has three desklamps controlled by 3 switches in the second room. The job of the person in the second room is to figure out which switches control which desk lamp.
Conditions:
Once the person leaves the switch room, he can not return (automatic, un-ajarable doors, and all that jazz). Nor can he see the room containing the desk lamps from the switch room. The lamp room is completely sealed - no light can escape the room in any way. There are no accomplices, robots, or other mechanical aids. Each switch controls one, and only one, lamp. Each switch is binary - on and off, no dimmer or other intermediate settings.
Sorry 'bout that whole damn hat thing. I’ll have it straightened out by Monday at the latest… 
Query: Does the man have hands? If he’s armless, I don’t know the answer.
I am also assuming that the lights/switch relays are in perfect order and that the lamps aren’t attached to any sound devices or anything untoward like that.
This one is easier, and this is solved the same basic premise I was using to figure out the hat thing: barring primary visual information, you have to move on to the other senses and/or secondary visual information.
Okay. Guy flips the first two switches in the control room and leaves the last one alone, then waits a minute or two. Before he leaves, he cuts off one of the switches (let’s say the first one) and leaves the middle switch on. Then he takes a leisurely stroll down the hall.
When he goes into the room with the lamps, only one lamp should be burning. He knows that the switch he left on controls that one. He then feels the light bulbs on the remaining two lamps. One should be warm; that’s controlled by the first switch. The last one, the one he never cut on, should be cold.
Don’t knock smoking crack until you try it. That’s the only way I can grasp Hegelian theory.
Person #3 DOES know the colour of HIS hat, he would know everything if he knew the colour of the hat behind him. If he knew the person behind him was sweating as much as he was, the puzzle would be solved.
Dr_Paprika’s right; it’s up to persons 3 and 4 to figure it out. No. 3 can deduce more than I realized.
This is the configuration of the puzzle as it stands:
B | W B W
But suppose it was like this…?
B | W W B or W | B B W
Then there would no problem here. If everyone is reasoning this the same way, they would know that no. 4 would immediately see that the two guys ahead of him are wearing the same color hats, so he and the guy on the other side of the wall must be, by deductive reasoning, wearing the opposite color hats. That would stump them for all of six seconds before they got out. Since they aren’t free yet, you can eliminate those possibilities.
Likewise, these guys know that if they alternate 2 types of hats among 4 of them, you would get 6 different positions. That leaves four possible configurations. They must be either THIS… configuration “A”…
B | B W W
… configuration “B”…
W | W B B
… this one…
W | B W B
and the right answer, configuration “D”…
B | W B W
Guy no. 4 knows he can safely eliminate “A” and “C”. They don’t jibe with what he sees.
Guy no. 3 must have arrived at much the same conclusion. Since he’s so smart, he has safely eliminated the same four possibilities as no. 4 did. So he knows he MUST be wearing a black hat because if he was wearing a white hat they’d be gone by now.
Guy no. 2 has likewise arrived at the same conclusion as nos. 3 and 4, taking a bit longer. He knows HE is wearing a white hat and the guy immediately behind him is wearing a black hat. It’s the only possibility that exists.
Even Guy no. 1 has figured out that there must be only two possibilities left among the six. The question is, how does either he or the last guy determine, with certainty, what color hats they are wearing?
THAT’S when Guy no. 4 looks down at the shadows on the ground. He begins to see heat waves imminating from B’s shadow; even though they haven’t been outside long, the hot sun is beginning to working a number on him. Since his own shadow is lacking those heat ripples and he doesn’t feel all that hot yet, he immediately realizes he and no 3. CAN’T be wearing the same color hat. With that, he screams out the correct configuration and the sadists who thought this up set them free.
Do you get wafers with it?
Re: KKB’s HATS riddle
KKB, the way you have worded the riddle makes it impossible to solve. IMPOSSIBLE. If any person’s hat has a 50% chance of being black or a 50% chance of being white, then looking at someone else’s hat gives you ZERO indication of the color of your own hat (assuming no reflective surfaces, etc).
If, however, you know that there are 2 white hats and two black hats, then you can get start using logical deduction. So, assuming they all know that there are 2 black hats and 2 white hats, the answer would be something like this:
If the set up is this:
B | W B W
The dude who wins is “B”, who is 2nd from the right. He knows his hat is black. How? He looks ahead and sees white. He also knows that the guy behind him can see 2 color hats. MEANING, if the guy behind him sees 2 hats that are the SAME color, he will know that his hat is obviously the OTHER color. Because this guy DIDN’T stand up, “B” knows that his color hat mustn’t be the same color as the guy in front of him. THEREFORE, he sees the guy in front of him having a white hat, his must be black. This is all, of course, assuming that they know there are 2 white and 2 black hats.
But the way the orginal riddle is worded, “LOGIC” can not solve it.
Ablett: Don’t say thaaaaaaaaaaaaaaaat, man. You know how much time I wasted on that riddle? 
Ablett & the others are right. It could jsut as well be 4 black or 4 white hats, it does not have to be 2 of each, according to the way it is worded- again- it appears something has been left out. It appears heat waves & temp differences are not part of the logic puzzle. OK< KKB, time for you to publish the “answer” and the reasoning behind it- then take your well deserved beating as we point out you are wrong.
::general sound of disgust::
The email from my coworker:
“If I understand your question right, I think you misunderstood the riddle. The puzzle was to figure out which man guessed the color of the hat on his own head, not the entire party’s hat colors. 3 realizes that his hat is black because otherwise 4 would have known for sure that his hat was black.”
Well, hell, if I knew that’s all I had to do, then it wouldn’t have been so damn hard…
Sorry all, our company’s notorious for having bad communication…