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Let's call De Bruijn n-phrase a sequence $S$ of n words $W_1 W_2 W_3... W_n$ such that any "left-rotation" of its words constitutes a correct and meaningful phrase. The left-rotations of $S$ are:

  • $W_1 W_2 W_3... W_n$
  • $W_2 W_3... W_n W_1$
  • $W_3... W_n W_1 W_2$
  • $...$
  • $W_n W_1 W_2 W_3...$

An (uninteresting) example of a De Bruijn 2-phrase is "work hard" / "hard work".

I don't know any example of a De Bruijn 3-phrase, but a more restrictive question of mine was answered with "someone I love" / "I love someone" (unfortunately, "love someone I" is not valid).

Challenge: find the longest De Bruijn phrase.

NB. Since I am a non-native English speaker, I would be grateful if you could paraphrase in plain English each left-rotation of your phrase.

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  • $\begingroup$ Do we have to use statements only or are mixed questions/statements allowed? Also, punctuation, etc. $\endgroup$
    – Alenanno
    Commented Oct 21, 2016 at 17:06
  • $\begingroup$ Since I don't know any good answer, any candidate would be appreciated! $\endgroup$
    – Aristide
    Commented Oct 21, 2016 at 17:07
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    $\begingroup$ This question with me does voice of Yoda remind! $\endgroup$
    – John
    Commented Oct 21, 2016 at 18:20
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    $\begingroup$ If my vote wasn't binding, I'd close this as "primarily opinion-based". Defining a "natural English word/phrase/sentence" is not easy to do, and it invariably leads to ambiguity. $\endgroup$
    – Deusovi ♦
    Commented Oct 21, 2016 at 18:37
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    $\begingroup$ I’m voting to close this question because open-ended puzzles are off-topic as of May 2019. This is not defined enough to turn it into a provably optimizable problem. $\endgroup$
    – bobble
    Commented Oct 29, 2021 at 17:48

9 Answers 9

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Using a bit of punctuation to make the meaning clearer.

De Bruijn 3

You go there.
There you go.
Go there, you.

De Bruijn 4

Move there quickly, Jack.
Jack, move there quickly.
Quickly, Jack, move there.
There — quickly, Jack — move!

De Bruijn 5

Now speak properly, Jack, ok?
Ok, now speak properly, Jack.
Jack, ok, now speak properly.
Properly, Jack, ok? Now speak.
Speak properly, Jack. Ok, now.

De Bruijn 6

Soon, anyway, Jack will come visit.
Visit soon anyway, Jack will come.
Come visit soon anyway, Jack will.
Will come visit soon anyway, Jack.
Jack will come visit soon anyway.
Anyway, Jack will come visit soon.

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    $\begingroup$ I'm not sure punctuation is allowed, +1 though $\endgroup$
    – Beastly Gerbil
    Commented Oct 21, 2016 at 17:17
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    $\begingroup$ @BeastlyGerbil Well, the punctuation is only to show how to read it. In spoken language there would be only words but intonation, etc. would be present to and it would change. :D Thanks though. $\endgroup$
    – Alenanno
    Commented Oct 21, 2016 at 17:18
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I suppose you could easily get up to 8 using

Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo.

This assumes that capitalization can be changed with each rotation (which makes sense, since you have to capitalize the first word of the sentence with each rotation).

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    $\begingroup$ @Aristide If you don't want this kind of answer, you could specify that $W_1 \neq W_2 \neq ... \neq W_n$. $\endgroup$
    – GentlePurpleRain
    Commented Oct 21, 2016 at 17:15
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    $\begingroup$ @Aristide I'm a native English speaker and it doesn't make much sense to me either. $\endgroup$
    – gtwebb
    Commented Oct 21, 2016 at 18:39
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    $\begingroup$ See the WP link in the answer. However, contrary to prescriptivist nonsense, this is not grammatical. $\endgroup$
    – R.. GitHub STOP HELPING ICE
    Commented Oct 21, 2016 at 19:49
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    $\begingroup$ Buffalo = a city, buffalo = animal, buffalo = to bully/intimidate. You can read it something like this: "Buffalo buffalo (buffalo from Buffalo), Buffalo buffalo buffalo (whom buffalo from Buffalo intimidate), buffalo Buffalo buffalo (intimidate buffalo from Buffalo)." It's weird $\endgroup$
    – halfmang
    Commented Oct 21, 2016 at 22:02
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    $\begingroup$ It's clear like this: Boston bulls Boston bulls bully bully Boston bulls. $\endgroup$
    – Florian F
    Commented Oct 22, 2016 at 8:55
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my attempt at 5:

1. my favourite things are puzzles
2. favourite things are puzzles? my!
3. things are puzzles? my favourite!
4. are puzzles my favourite things?
5. puzzles, my favourite things are

and my attempt at 6:

sounds like it should be hard
like, it should be hard sounds
it should be hard, sounds like
should be hard sounds like it
be hard? sounds like it should
hard sounds - like it should be

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    $\begingroup$ I'm a bit doubtful about #2 ... $\endgroup$
    – Rand al'Thor
    Commented Oct 21, 2016 at 18:31
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    $\begingroup$ "My!" is one of the possible contractions of "oh, my god!". That being said, I also think it's cheating. $\endgroup$
    – mr23ceec
    Commented Oct 21, 2016 at 18:34
  • $\begingroup$ The others being "My god!" ("my god, man, have you no shame?!" --Richard J. Field, Magellan's Cross p. 133 ) and "Oh, my!" ("lions and tigers and bears, oh my!" --Frank Baum, Wizard of Oz... allegedly) Also, "OMG", I guess. $\endgroup$
    – mr23ceec
    Commented Oct 21, 2016 at 18:38
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    $\begingroup$ Would be easier if we could hear these sentences being said. $\endgroup$
    – halfmang
    Commented Oct 21, 2016 at 18:39
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    $\begingroup$ Your attempt at 6 is very clever. Playing on the double function of "sounds" and "like" hides in plain sight some pleasant surprises, which are only revealed when the phrase is rotated. $\endgroup$
    – Aristide
    Commented Oct 21, 2016 at 19:34
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This won't break any record (and thus not close my question), but anyway:

  1. All kind men love.
  2. Kind men love all.
  3. Men love all kind.
  4. Love all kind men.

The meanings are clearly distinct, which IMHO is a desirable property, but I am not sure that the 3rd sentence is valid.

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  • $\begingroup$ I would change it to: "Men love all -- kind!" Meaning "Men do love everything, that's so kind of them!" $\endgroup$
    – yo'
    Commented Oct 22, 2016 at 13:03
  • $\begingroup$ @yo' My bad (English). I thought the meaning could be along the lines: "There are many kinds of food. Men love all kind." Is it correct? I would like to get rid of inner punctuation marks. $\endgroup$
    – Aristide
    Commented Oct 22, 2016 at 13:25
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The key to this puzzle is finding words that are more than one part of speech. Nouns that are also adjectives are especially good, since in English there's no limit to how deeply you can stack adjectives and there's no requirement for punctuation between adjectives.

For example, it's grammatically correct to say "Itsy-witsy teeny-weeny yellow polka dot bikini". You could add 50 more adjectives to that and although it would be awkward, it would be grammatical.

Andrew Ritz made a list of 54 words each of which is (amazingly) a noun, a verb, an adjective and an adverb. Since we know the pattern "adj adj adj adj ... adj noun" makes a valid English sentence, as long as we agree with his analysis of these words,that makes a 54-word de Brujin phrase.

Of course for this puzzle, we don't need words to be 4 parts of speech, just 2 -- adjective and noun. It's easy to come up with more words that are both: cooler (more relaxed, a drink container), sick (awesome, vomitus), red (color, a communist), green (color, an environmentalist), cricket (fair vs. an insect), tough (rugged, a thug), concrete (not abstract, artificial stone) etc.

Adding the 7 I just rattled off to Andrew's list, here is a 61-word de Brujin phrase:

back best better bitter broadside clean clear close cod collect concrete cooler counter cricket crisscross damn double down even express fair fast fine firm flush forward free full green home jolly last light low o.k. okay out pat plain plumb plump pop quiet red right rough round second short sick solo square steady still tiptoe tough true upstage well wholesale worst wrong zigzag

By finding more noun-adjectives, this could go on forever. I would guess there are several hundred such English words. There's probably an exhaustive list of these somewhere on the interwebs.

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    $\begingroup$ the phrase should be "correct and meaningful". Can you describe to me the meaning of a few of the examples in the 61-word de Brujin? $\endgroup$
    – djechlin
    Commented Oct 23, 2016 at 21:35
  • $\begingroup$ ... except that the order of adjectives means you can't rotate them unless they're all in the same category. $\endgroup$
    – user52889
    Commented Oct 23, 2016 at 22:50
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If you string together a bunch of verb/noun players you can really make this a mess. I'm not saying it all works, (it actually does) but you get the idea:

Friends critique transition workshop text.
Critique transition workshop text friends.
Transition workshop text friends critique.
Workshop text friends critique transition.
Text friends critique transition workshop.

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  • $\begingroup$ "colorless green ideas sleep furiously" is the canonical example of a syntactically valid sentence that lacks meaning. You've succeeded at syntax, not meaning. $\endgroup$
    – djechlin
    Commented Oct 23, 2016 at 21:36
  • $\begingroup$ @djechlin, Sorry, just saw this. Although true, that is a fine example of a meaningless sentence, there is meaning in each of my sentences even though they may be awkward. They each have meaning and alternate between declarative and imperative style sentences. Look a little more closely. $\endgroup$
    – John
    Commented Mar 16, 2017 at 21:44
  • $\begingroup$ Are these even syntactic? I don't even see how to assign POS to the first one. $\endgroup$
    – djechlin
    Commented Mar 16, 2017 at 21:47
  • $\begingroup$ @djechlin, "Who critiqued the transition-workshop's text?" :) Hyphen added for clarity. $\endgroup$
    – John
    Commented Mar 16, 2017 at 23:17
  • $\begingroup$ Eh, I think you see why I think this doesn't count. Carry on. $\endgroup$
    – djechlin
    Commented Mar 16, 2017 at 23:48
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My attempt at 8:

Jack, Google "Jill" now. Jill, Google "Jack" now.
Google "Jill" now, Jill. Google "Jack" now, Jack.
Jill, now Jill, Google "Jack". Now, Jack, Google!
Now, Jill, Google "Jack". Now, Jack, Google "Jill".
Jill, Google "Jack" now. Jack, Google "Jill" now.
Google "Jack" now, Jack. Google "Jill" now, Jill.
Jack, now Jack, Google "Jill". Now, Jill, Google!
Now, Jack, Google "Jill". Now, Jill, Google "Jack".

I'm thinking that speaking and names might lead to a longer one. But I agree with Deusovi that the "natural" sound of some sentences is subjective.

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  • $\begingroup$ Yes, it seems that such phrases can be extended ad libitum. You could even say: Google "Google "Google "Google ... """". $\endgroup$
    – Aristide
    Commented Oct 21, 2016 at 19:42
  • $\begingroup$ I considered something like that, since any phrase might be something Googled (regardless of its meaningfulness). I did try to create one that I thought was fair, though (i.e., only Googling the individual words). $\endgroup$
    – elmer007
    Commented Oct 21, 2016 at 19:44
  • $\begingroup$ @Aristide or of course "Buffalo..." $\endgroup$
    – Chris H
    Commented Oct 24, 2016 at 8:32
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There is one $3$ from my previous answer to your other question which works (the others don't):

Right side on / Side on right / On right side

And a $5$ (added punctuation to show pronounciation):

What if I was to..?
If I was to, what?
I was to, 'What if?'
Was to 'What if I?'
To 'What if I was?'

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  • $\begingroup$ Do you mind adding the paraphrasing to examples number 3 and 4, and maybe 5? Thanks. :D $\endgroup$
    – Alenanno
    Commented Oct 21, 2016 at 17:25
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    $\begingroup$ I don't think your 5-word phrase works. Numbers 3, 4, 5, are not valid phrases, and number 2 is questionable. $\endgroup$
    – GentlePurpleRain
    Commented Oct 21, 2016 at 17:39
  • $\begingroup$ @GentlePurpleRain yeah I admit it is dubious $\endgroup$
    – Beastly Gerbil
    Commented Oct 21, 2016 at 17:43
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so and yet are conjunctions which can also be adverbs.

So let's start with a simple four-word De Bruijn:

so many go back: Lots of things return

many go back so: Lots of things return like that

go back so many: Move backward this amount

back so many go: Lots of things return

So nothing spectacular yet. Yet let's keep going.

yet so many go back: But lots of things return

many go back yet so: Lots of things still return like that

go back yet so many: Move backward even this amount

back yet so many go: Lots of things return again

so many go back yet: Lots of things return again, nonetheless

Yet we can do so much better (10):

yet so many go back, yet so many go back: But lots of things return, but lots of things return. (as if these things are contradictory, but they are tautology)

many go back yet, so many go back yet so: Lots of things still return, therefore lots of things still return like that

go back yet, so many go back, yet so many: Move backward now, in order that lots of things return even though they are great in number

back, yet so many go back yet, so many go: I have returned, however, lots of things return again, therefore lots of things depart

so many go back yet, so many go back yet: Lots of things return again nonetheless, therefore so many return again nonetheless (simple tautology)

The other five rotations are identical to the five yet described.

So you might see we can add more phrases with yet and so being the conjunctions. It might continue forever so.

Of these four cases, the first and last will repeat infdeinitely; it's less obvious that you can do it with the middle three, so let's try one more repetition yet:

many go back yet, so many go back yet, so many go back yet so

Lots of things still return, therefore lots of things still return, therefore lots of things still return like that

go back yet, so many go back, yet so many go back, yet so many

Move backward now, in order that lots of things return even though lots of things return, even though they are great in number

back, yet so many go back yet, so many go back yet, so many go

I have returned, however, lots of things return again, therefore lots of things return again, therefore lots of things depart

So I think we can just keep adding more repeats to this five-word phrase and the phrase will continue to be structurally sound. Whether you derive much meaning from it is another question.

Of course, there are also simpler sentences in natural English which are indefinitely repetitive; although you might consider them trivial and not in the spirit of the question, the spoken word often has inflection, tone and nuance which the written word cannot readily communicate:

No, no, no, no, no, no... no.

-- Jim Trott

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