Sideblaggin'

A note on today’s comic: Judging from my inbox, a lot of people have a different perspective on the GRY puzzle than me. First of all, I believe it’s a fairly old riddle. But more importantly, I think that originally the “English Language” bit wasn’t even a part of this riddle. It was just a head-breaker because there was no answer. But then someone who thought they were oh-so-clever came up with the idea that somewhere in the puzzle it could be read as asking what the third word in the actual phrase “the English Language” was. That’s a pretty lame interpretation. There have been lots of rewritings of the puzzle to try to make it work a little better, but they’ve never removed the lameness. Some of them more friendly to that stupid interpretation than others. I’d been hearing the angry/hungry puzzle for years (and talked about the interesting fact that there was no answer) before I ever heard someone try the “language” thing. Snopes has a good article on this puzzle.

I always hated those ‘lateral thinking’ puzzles — the ones where they said “oh HO, I never told you that the doctor’s mother was a midget and this was all happening a space station! Don’t you feel dumb now?‘ Because once I figured out that language was really, really flexible and imprecise, it seemed that the key to communication was just figuring out what they probably meant. And figuring out what they could possibly mean if you use all the wrong definitions and stuff is interesting, but I don’t think it teaches all that much more than bad communication. These should be kept very separate from actual logic puzzles, which are really neat. There’s a thriving section for them on the forums, and a lot of people found my site looking for the answer to the Blue Eyes puzzle (which is great because it doesn’t use trick language anywhere — indeed, I’ve rewritten it over and over to make it as unambiguous and clear as I can — and yet the answer is incredibly elusive).

112 thoughts on “Sideblaggin'

  1. i agree that these lateral thinking puzzles should be kept separate from what you see as more traditional logic puzzles. at the same time, i think that they’re valuable in terms of stretching a person’s thinking and training the very useful skill of questioning one’s own assumptions. more specifically i think it’s realizing that we are always making, and generally remaining oblivious to, those assumptions that is most helpful.

  2. i think it’s pretty obvious that there is an answer.

    the first word is angry.
    the second word is hungry.
    and the third word is ANGRY.

    ok so it’s lateral. grrrrr.

  3. i think ‘nangry’ as an alternative to angry would be better, i might start using it and see if people notice.

  4. I loved today’s puzzle – that’s exactly how I feel about communication. The best part is the guy screaming in pain throughout, while the other guy communicates the “moral of the story”.

    Ahh, your cartoons bring me such enjoyment. :D I can’t even explain on how many levels this cartoon makes sense!

    Sara, I agree in a way. But they’re useful mainly because they’re used – another words, because people can’t always be trusted and will purposefully try to trick even their friends, we must learn not to trust other people’s words to mean what they should mean. While you’re right it’s a valuable lesson, that doesn’t mean it should be a valuable lesson, or that it is a good lesson to have to learn.

  5. I still don’t get it. Unless it’s

    *SPOILERS*

    that the only 2 things that really matter are hunger and anger. Or something along those lines. As for the blue eyes thing, I just checked it out, and unless I’m just not getting it, doesn’t everyone have brown eyes except for 1 person? The person that’s left deduces that they have blue eyes, and leaves the island the NEXT night.

  6. You should take the word “inductive” out of the Blue Eyes puzzle. If that hadn’t been there, I wouldn’t have gotten it, but it was, so I did.

  7. starshine_diva, read it again. The second paragraph states that there ARE 100 of each eye color; that fact just isn’t known to the islanders.

  8. [/b] Just seeing if I can turn off this goshdang boldness. I don’t know whether you use HTML or BBCODE here so I’ll just do both.

  9. Step, I disagree that the use of lateral thinking puzzles is so confined to trust issues. Being aware of the fact that we make assumptions about *everything* affects directly the way that we subsequently interact with the world. If we did this more regularly in real life — that is, questioning the premises that we’re basing our generally automatic assumptions are — then we’d probably end up making fewer stupid decisions that lead us to suboptimal conclusions.. :)

    In fact, part of what I love about math is that we are trained (ideally) to identify and be able to describe the assumptions that are underlying any context that we’re exploring. I’m always surprised to meet mathematicians who don’t look at the world that way too, but..

  10. Great site, nice puzzle too.

    If I can only see brown eyes, and the Guru says “I can see someone with blue eyes”, then I know that I have blue eyes, so I leave the island.

    If I can only see one pair of blue eyes, and that person does not move, it’s because they can see a pair of blue eyes, so I must have the other pair of blue eyes, so I (and they) know that we have blue eyes.

    If I can see 2 pairs of blue eyes, and they don’t move, then that is because they can see another pair of blue eyes, which must be me, so all three of us leave.

    Etc ….

    Nice puzzle. The key is in the 2nd statement: “They are all perfect logicians — if a conclusion can be logically deduced, they will do it instantly.”

  11. The 3rd is “atgry” ( http://en.wikipedia.org/wiki/At_sign ). It was the name made up to solve 2 literary puzzles, the one in this comic and finding a word that rhymes with “orange”, as the plural or “atgry” is “atgrynge”.

    And yes, it is obscure, so it might not be a very good answer. But together we can thrust it into popularity and defeat the English language communist rebels once and for all!

  12. This comic made me laugh so much!
    Maybe it was because I like it when there’s blood at some point of any story.
    (?)
    Well the thing is that I didn’t know about this riddle or any other in your language. I didn’t have to think at all to realize what it was anyway. I looked it up tho. just to read what english speakers say.
    Some of them are real stupid.
    But there are some quite good riddles that can really make you go crazy trying to figure’em out. Those are the ones I like.
    I would get to the point right now, but I’m afraid I forgot which it was.
    It’s good. Now I want to read as many good riddles in english as I can find in my magic box.
    Then I’ll shut my boyfriend’s mouth if he wants to mess with my mind telling crazy riddles in english. muaha ha ha.

    Sos un capo chabon.

  13. Dave K: Thanks — but I don’t know if that’s really the original form, and if it is, I still insist it’s a dumb form. The “gry” riddle alone probably predates it, and if it doesn’t, it’s separated from it since then, and it’s routinely put together badly. To me, it’s an example of the sort of obnoxious thinking that encourages people to ignore logic in favor of twisting language.

    From the article:

    “You might be tempted to say something like: “That can’t be the right answer. It’s too stupid!” Hey, remember that most riddles ARE “stupid.” For example, there’s an old riddle which asks: “What is Bozo the Clown’s middle name?” (The answer is “the.” Now THAT’S “stupid”!)”

    Not all riddles are stupid, but he’s right about this one. The base “gry” riddle, the one with no real answer, is a lot better.

  14. I’d just like to point out that this puzzle doesn’t actually work—Angry and Hungry clearly aren’t the first two words–The and English are. Technically, it doesn’t make sense.

  15. I’d just like to say, as a web developer, I think wordpress is lame for not doing something about the <b>.

  16. grepping a big wordlist turns up

    aggry
    ahungry
    angry
    anhungry
    hungry
    unangry

    I’ve certainly heard unangry in real speech. Only one citation in the OED, though:
    1876 MORRIS Sigurd II. 159 “Look down with unangry eyes on us to-day alive.”

  17. Sara, I agree with you on many levels. However, I’m one of those people who takes things really seriously, and I remember hating all the times my “friends” in H.S. would tell me something, trying to see how “gullible” I was. I’d rather learn about assumptions through valid challenges of their points and thinking, not in having to question every single word they say or “fact” they may have offered up. Another words, if the only way to know they’re trying to trick me is to say “I think you’re lying about x”, I think that’s just plain rude, dumb, and a waste of my time – NOT a good lesson in assumptions.

    But like I said, this is just me, I’m playing the contrarian, and I generally avoid joking with friends because I believe there’s always some truth behind it, and it’s a way to hurt someone and laugh about it, which I don’t like. So you can see I’m not approaching the question in the standard manner. :D

    Note: I’m disappointed someone put the answer to the Blue Eyes puzzle in the comments. It would be nice if you removed it, as I was planning on thinking it through this weekend. I was already stumped on one point: how did the Guru possibly add any information to the island? I haven’t had time, though, to really think about the puzzle at all, and had wanted to do so once I headed off camping. Oh well….

  18. I’m missing something about Steve Parker’s answer to the Blue Eyes puzzle. This part in particular:

    “If I can see 2 pairs of blue eyes, and they don’t move, then that is because they can see another pair of blue eyes, which must be me, so all three of us leave.”

    How does that prove that you have blue eyes? IF you see two pairs and they don’t move, it could be because they see EACH OTHER, and thus you still have no idea what color your own eyes are.

    What am I missing?

  19. You might be interested in taking a look at Zendo: http://www.wunderland.com/WTS/Kory/Games/Zendo/index.html

    It’s a induction logic game (not unlike Eleusis) where you have to find a secret rule one of the players has created. The whole “bad communication” theme disappears, because the output from the Master is binary (a given arrangement of pieces satisfies the rules or not), and you can make experiments to clear up any corner cases on your theories.

  20. I have a problem with the Blue Eyes puzzle as it’s currently written: nothing says that the Guru’s statement is truthful. As far as the solver is concerned – or, more importantly, as far as the island’s inhabitants are concerned – the statement could well be false. For the intended solution to hold, it must be made clear that (1) the Guru is incapable of speaking untruthfully and (2) the other island residents are aware of this fact.

    It would also be helpful to explicitly specify that not only are all the inhabitants perfect logicians, but that they KNOW they are all perfect logicians. This is implied by the “all the rules” statement at the end of the first paragraph, but the statement that they are all perfect logicians, despite it being a “rule” of the puzzle, isn’t a “rule” from their perspective – it’s just a statement of fact. For the solution to work, they need to know that all other inhabitants are flawless in logic. This ambiguity over the term “rule” should be eliminated.

    Actually, if I’m being nitpicky, I also need to be assured that no one on the island is blind or color-blind, and that all the inhabitants know this as well. But that’s really a lateral issue.

    If we are given those, then yes, all the blue-eyed residents get to bail on the hundredth night. What Josh Paulik is missing is that everyone on the island is capable of the same level of logical deduction – namely, a flawless level. Let’s say there are only three blue-eyed people on the island, and we’ll name them Aoi, Blue, and Cyan. [Go ahead, boo me.] Here’s Aoi’s diary:

    Day 1: The Guru basically said that there’s at least one blue-eyed person on the island. All these years I waited and big help that proved to be – I already know that. Blue and Cyan both have blue eyes. I see that myself. It’s nothing I don’t already know…

    Day 2: I saw Blue and Cyan today. They looked deep in thought. They’re probably thinking about what the Guru said. Obviously, if there’d been only one person on the island with blue eyes, e would have left last night – e’d see there was no one else the Guru could have been referring to. So everybody knows that there are at least two people out there with blue eyes. Again, big deal. I even know who they are. They’re the only two with blue eyes that I’ve seen on the whole island… They’re probably looking at each other, realizing they’re the only two with blue eyes, and will be leaving tonight, the lucky bastards.

    Day 3: Blue and Cyan are still here! If either of them saw no one else with blue eyes, they’d have left last night. This can only mean that there are at least THREE blue-eyed people on the island. But I’ve seen everyone else, and nobody has – wait a minute – HOLY SHIT, I MUST HAVE BLUE EYES! It’s the only explanation for them still being here! Time to pack my things – I’m off this island tonight! Blue, Cyan, save me a seat on that ship, cause we’re sailing off together…

    This same logic expands out indefinitely. Each day that passes after the Guru’s statement that no one leaves, everyone learns that the number of blue-eyed people on the island is at least one greater than the minimum value they had yesterday, as otherwise they’d have left.

    Here’s my favorite version of these “colored hats” problems: Four perfect logicians, each with perfect sight (including color) and perfect speech, all of which know that all of them are perfect logicians with perfect sight (including color) and perfect speech, are being held prisoner. I’ll name them Allyn, Byrne, Chyna, and Dyson. All four are strapped to electric chairs, which are arranged in a line such that (1) Allyn can see Byrne and Chyna, (2) Byrne can see Chyna, and (3) none of the other nine possibilities of one seeing another exists. [Dyson's chair is behind Allyn's, but it's facing backwards.] Their captor, Edgar, is someone they all know is incapable of speaking untruthfully. Edgar says to them: “I have four hats here – two blue, two red. I’m going to put one on each of you, distributing the colors randomly. I’ll place them such that you can’t see the color of your own hat, but for all others you can see, you can see what color hat they’re each wearing. Once I place the final hat, you all get fried in ten seconds unless the first word any of you speaks is the color of the hat the speaker is wearing. Of course, you can’t communicate in any other way or you will be fried (you don’t need to know how I’ll be able to tell – you know I’m speaking the truth). If the first word spoken by any of you is the correct hat color of the speaker, you will all be spared and free to leave.” Assuming they all prefer being freed to being fried, is their escape guaranteed? If so, how? If not, under what circumstances (if any) can they escape? – ZM

  21. Damn it, I forgot something: Allyn, Byrne, Chyna, and Dyson all know the seating arrangement. Each knows what the others can see. (They apparently shared that info before Edgar arrived.) Yes, that changes the answer. – ZM

  22. Got the answer to your riddle, Zot-

    (I’ll just say A, B, C, and D, as I’m too lazy to go back and look at their names)

    A can see B and C. B can only see C. D can’t see anything.

    If B and C both get the same color (red or blue), then A will know that he has the opposite color, as there are only 4 hats (2 of each color).

    If B and C get one of each color, A can’t say anything, because he can’t be sure. Since B is a perfect logician, he’ll realize that since A couldn’t be sure, B and C must have two different colored hats. So B will look at C’s hat, and know that his hat is the opposite color.

    So either A or B save the day. Poor D and C just sort of stare off into space, sweating bullets.

  23. You are completely correct, RM. That’s why I always hated those stupid Mensa puzzles. They’re never logic-based, all with their lots of possible interpretations and stupid unclosed holes. “Guess what we’re thinking!”

    As a related note, I’ve always felt that people who say “When you assume, you make an ass out of you and me” should really just shorten it to “When you assume, I’m an ass.”

  24. Hardest Logic Puzzle? Really? Is there an objective measurement to this or just a subjective title?

    It took me like 10 seconds to guess the answer, and then another couple of minutes to verify it.
    The first 10 seconds: Looking at it, it’s obvious that brown eyes nor guru can possibly leave based on that one statement, since the only color mentioned is blue. Thus, some number of blue eyed people must leave. Since they are all identical and indistinguishable as far as the problem goes, it’s an all or nothing proposition–they all have to leave at the same time or never leave. So, now it’s just a matter of when all the blue eyed people would leave. Since it can’t be first night, it’s probably the 100th night.

    Then to verify, just have to think what happens if there’s 1 blue eyed guy, he’d see no other blues, and know he’s the one. If there’s 2 blue eyed guys, each would see one other. Each would know that if the other guy saw no other blues, they’d leave the first night. Since neither guy left, they know there must be one other blue eyed guy, namely self. If there’s 3 blue eyed guys, They’d do the same logic as with 2 guys, except it’d take an extra day. etc etc.

  25. I’m still not getting the blue-eyes puzzle.

    I don’t see why any of the blue-eyes would realize they had blue eyes if there were 99 other people with blue-eyes. To a person with blue-eyes, they would think, “obviously, blue-eyed people 1-99 aren’t leaving ’cause they all can see 98 other people with blue-eyes!”.

  26. A couple weeks later to the last poster….

    I don’t see why any of the blue-eyes would realize they had blue eyes if there were 99 other people with blue-eyes. To a person with blue-eyes, they would think, “obviously, blue-eyed people 1-99 aren’t leaving ’cause they all can see 98 other people with blue-eyes!”.

    Come at it from a different direction.

    If there was one blue-eyed person, she’d see no one else with blue eyes and leave the first night.

    If there were two blue-eyed people, each would see the other. They would know that if the other person was the other one, he would leave because of the line. That doesn’t happen, so they both have to conclude they are each blue-eyed and leave that second night.

    If there were three blue-eyed people, each would see two. They all know that if those two are the only two blue-eyed people they would behave as above. There must then be another blue-eyed person. They all realize it is them and can leave that third night.

    If there were four, they would know how three blue-eyed people behave (above). When that doesn’t happen….

  27. But it says the all instantly arrive any logical conclusion, so therefore all 100 blue eyes would instantly leave that night.

  28. No, because they don’t have all the information yet. They can’t find out that nobody else is leaving until the next day, and this has to happen 100 times before they have all the information they need.

  29. Guru doesn’t have to have a unique eye color, and he doesn’t have to be as specific as that. He can simply say (and be believed) that he knows there are at least two different eye colors among those on the island. Now all the persons of both colors gain knowledge equally, so the problem works the same way except that, assuming the numbers of both are balanced and not 1 of each, all 2n people (everyone except Guru) leave on the nth day. (If they aren’t balanced, then the smaller group all leave on the day equal to their own n, and all those of the other color — again except Guru, whatever color his own eyes — leave the next day.)

  30. Could someone explain this angle to me:

    A has blue eyes.

    After the first night, nobody leaves the island, therefore the number of blue-eyed people is not one. However, everyone already knew this, therefore there is no new information because nobody left. Therefore, everyone is in exactly the same position with regards to information content that they were in before. Therefore, there’s no way any of them could be one day closer to leaving. I agree that the induction argument is persuasive, but I’ve managed to convince myself it doesn’t work, even though I can’t properly explain why.

    This reminds me of the puzzle, which is probably as close to explaining why I don’t think the blue eyes puzzle works as I can manage:
    A prisoner is sentenced to be executed on some day in January. He is also told that on the day of his execution, he will not know that it is the day of his execution.

    Without his knowledge, the warder randomly selects the 17th.

    The prisoner sits and reasons that it can’t be the 31st, because if the 31st rolled around, he would know it was going to be that day, violating what he was told. He then reasons that it can’t be the 30th, because since it can’t be the 31st, he would know on that day. He continues this inductive chain of reasoning and comes to the conclusion that there is no day in January that he could be executed.

    He is executed on the 17th, as planned.

    Where is the flaw? I don’t know …

  31. “Guru doesn’t have to have a unique eye color, and he doesn’t have to be as specific as that. He can simply say (and be believed) that he knows there are at least two different eye colors among those on the island. Now all the persons of both colors gain knowledge equally, so the problem works the same way except that, assuming the numbers of both are balanced and not 1 of each, all 2n people (everyone except Guru) leave on the nth day. (If they aren’t balanced, then the smaller group all leave on the day equal to their own n, and all those of the other color — again except Guru, whatever color his own eyes — leave the next day.)”

    It would have to be “exactly two different eye colors”, not “at least two”. If it was at least two, then there could be a single person with a third color (green, red, whatever), and if such a person existed he would know that of the at least two colors, blue and brown were included, but he could not include his own color which he could not see. Likewise, everyone else would see three colors and think, well, maybe I’m that third color, so they wouldn’t behave in a manner that would give the one person with red eyes any information. If it’s “at least two colors”, everyone has to assume that situation as a possible case, and no one gets anywhere. If it’s exactly two, then everyone can rule that out and the logic follows normally from there. The eye color of the guru is irrelevant, and the guru never gets to leave.

    @ Richard Brown:
    The stupid answer? He could be executed on any day once he’d decided that he couldn’t be executed at all, since he certainly wouldn’t expect it at that point ;)

  32. What if one of the brown-eyed people thought he himself had blue eyes? Wouldn’t the entire chain be ruined?

  33. No, because he’d see one more set of blue eyes than the others. (Blue eyed people see N(blue)-1 people). So, while he might have made that error, he could only make it the day after all the blue eyed people had left.

    Now, if he knew that there were only blue and brown eyed people on the island, he could then leave the next night; he knows that his eyes are NOT blue, but unfortunately the possibility of green eyes would trap him.

  34. @ Richard Brown:
    The piece of information that the guru added to island was not “Someone has blue eyes.” As you say, the people on the island already knew this. However, they did NOT know that everyone else knew this. The guru basically took information that everyone knew privately and made it public. As soon as everyone knows that everyone knows, the chain of inductive reasoning begins.

  35. “However, they did NOT know that everyone else knew this.”

    Sure they knew this. Basic math, the most anyone can ever see is one more or less pair of blue eyes than you see. We only need to have three people on the island with blue eyes for everyone to know that everyone can see a pair of blue eyes.

  36. To see why the guru’s statement is important, let’s consider the case where there are only two people on the island, and both of them have blue eyes. Obviously, as each can see the other, each of them know that there is somebody with blue eyes on the island. However, as they do not communicate, and they do not know their own eye color, they do not know that the other also knows that there is somebody with blue eyes on the island. What they don’t know is the state of mind of the other person – there is no way for A to determine what B knows about A’s eye color.

    Then the guru speaks, and informs the two that there is somebody with blue eyes on the island. This information allows A to determine what B knows about A’s eye color. If B knows that A does not have blue eyes, then B will determine that the one with blue eyes is him, and he will communicate this fact by leaving the island. When B fails to leave the island, he communicates that A has blue eyes to A – and vice versa. What the guru does is enable each person to communicate his knowledge about the other’s eyes by either determining or failing to determine his own eye color.

    In the general case, what each blue-eyed person communicates by staying n days is that there are at least n + 1 people with blue eyes. When n + 1 is equal to the number of blue-eyed people on the island, this communicates to each blue-eyed person that in addition to the blue-eyed people they can see, there is one blue-eyed person they cannot see – and that person is them. Until the guru speaks, however, staying a day does not communicate anything. It is the guru’s statement that allows islanders to reason about each other’s knowledge of their own eye color.

    It is worth noting that in this formulation, the number of people who do not have blue eyes is completely irrelevant.

  37. I propose that the guru could say nothing, and EVERYONE would leave (with the exception of the guru him/herself) on the 100th day.

    On day one, you know that everyone sees at least 1 brown eyed or blue eyed person, and on day 100, you know that there are at least 100 of both. Therefore, you know that your eyes are either blue or brown.

  38. When I said, “Therefore, you know that your eyes are either blue or brown.” I meant you would know which one they were specifically.

    Imagine for a moment, you are the blue eyed person. On day 100, the brown eyes haven’t left, telling you there are at least 100 (which you knew already). Also, you know there has to be at least 100 blue eyes, because if your eyes were, say, purple, they would have left on day 99 (since they knew there were at most 99 and at least 98).

  39. Re: Trevel and Robert Brown…

    I had the same problem you guys did. I felt the power of the inductive argument, but I kept getting tripped by, “But, no new information is being added!” I think I’ve finally convinced myself, and here’s how.

    The situation when one person has blue eyes is pretty obvious, I hope everyone gets that one.

    The logic for two people is straightforward, too. Let P be the proposition, “Someone on the island has blue eyes.” For this example, Aoi and Blue will be our blue-eyed guests. Clearly, P is true. Furthermore, Aoi knows P is true. (He can see Blue.) However, Aoi *doesn’t know* if [Blue knows P is true]. (I’m using brackets for nesting.) From Aoi’s perspective, Aoi might have brown eyes, which would mean that Blue didn’t know P *until the guru spoke*. That’s the magic ingredient – even though everyone knew the thruth of P from the beginning, her saying it to everyone allows Aoi and Blue to leave on the second night.

    Now, I followed that easily from Zot’s description. However, I was still unconvinced for the third case, hopelessly hung up on the belief that no new information was being added. But it’s all about meta-knowledge. Here’s how it goes for Aoi, Blue and Cyan:
    Aoi knows P is true. Aoi knows [Blue knows P is true]. (Aoi sees Cyan, and thus knows that Blue can, too.) But Aoi *doesn’t know* if [Blue knows [Cyan knows P is true]]. Aoi has to assume that he might have brown eyes. In that case, Blue would only see Cyan’s blue eyes and thus be unsure of whether Cyan would leave on the first night. Thus, Aoi is unsure if Blue will leave on the *second* night.

    Note that, for the three person case, not only does everyone know that there are blue eyes, but everyone knows that everyone knows! (In other words, everyone knows that no one’s leaving on the first night.) However, not everbody knows that everyone knows that everyone knows, you know? :) And that’s why, for the full problem, everyone knows that they’re stuck there for at least 99 days. However, every day pops one “X knows that Y knows” off the stack, bringing the day of certainty closer.

    I hope that clears things up for someone who was stuck in a similar rut. :)

  40. Another explanation with the same answer
    Everyone can count, right? So everyone knows the number of blue eyed people they can see. The question is if there is one more or not.

    So, if you see no one with blue eyes, you are the only one.
    If you see one person with blue eyes, and that person didn’t leave the first day, because they saw another one with blue eyes, you leave also.

    If you see two people with blue eyes and it’s day three, you’ll leave.

    Basically if you see n-1 blue eyed people, you’ll leave at day n.

    The others can’t leave, since they don’t know what color they really have. They have no idea, that there are only two other colors. For all they know, they could have rainbow colored eyes…

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