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This was inspired when I tried to solve BmyGuest's Owls at sunset - find the odd one out

Similar to that group, these birds have gathered prior to a hunt albeit an evening hunt instead of a dawn foray. However, the Strigiformes gathered here have a different group system. Not only do they have different rules to follow, but they don't mess around with sho-who-whoing outsiders away. Imposters are torn to shreds and fed to the hawks as payment for staying out of the owls' hunting area. Sadly, this has not led to increased security. This group has two outsiders in their midst.

Can you identify the two owls behaving anti-socially (I.E. not following the parliament rules) in the image below? What is the rule?

A valid answer must contain the parliament rule and why those particular owls are not following it. The puzzle can be solved with a black-and-white printout of the image.

Different-Owl-Picture-Hi-BmyGuest-I-Hope-You-Like-This-Shoutout

Note 1: In the column labels, I skipped the letter I on purpose to avoid confusion with the number 1. It is not a clue.

Note 2: BmyGuest found a valid pattern that I missed. The owls he found are, in fact, the odd birds out. I have since changed those two bird eyes such that they are still outside the intended pattern but no longer fall under the pattern BmyGuest found. I have delivered +1 to that answer nonetheless.

The one two and only hints:

I added a row of owls simply because I liked how the pattern broke there. It doesn't really matter how many owls there are. The pattern holds up for any positive natural number of owls. Therefore, they must be following a pattern or series.


There are 64 possible eye pairs. Only 30 are valid and only 18 are used in the picture.

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    $\begingroup$ Is the owl parliament a reference to Fez by any chance? $\endgroup$
    – xnor
    Jun 25, 2015 at 21:15
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    $\begingroup$ @xnor I don't understand that reference. A group of owls is called a parliament. That's where I got the name. $\endgroup$
    – Engineer Toast
    Jun 25, 2015 at 21:55
  • $\begingroup$ I'm pretty confident that your 2nd hint is wrong. There are only 18 different patterns in your picture. (There were 20 before you took the two special owls out.) $\endgroup$
    – BmyGuest
    Jun 30, 2015 at 14:26
  • $\begingroup$ Aha! You're right, @BmyGuest. I went back to my source data sheet to do the count. $\endgroup$
    – Engineer Toast
    Jun 30, 2015 at 14:27

5 Answers 5

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The odd ones out are

A2 and D7

Explanation:

The pattern is semaphore. Use the directions of each owl's eyes as the positions of the flags.

 HUSHLITTL
 OBABYDONT
 SAYAWORDM
 AMASGOING
 TOBUYYOUA
 MOCKINGBI
 RDITTHATM
 OCKINGBIR
 DWONTSING
These are the lyrics to the lullaby "Hush Little Baby".

A2 and D7 are the wrong letters. A2 should have looked south, northeast, and D7 should have looked south, east.

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  • $\begingroup$ Did you mistype, or is B9 wrong also? $\endgroup$
    – Bailey M
    Jul 2, 2015 at 17:44
  • $\begingroup$ Did you mistype Bailey, I think you meant C9. C9 is definitely O. I fixed it. $\endgroup$
    – LeppyR64
    Jul 2, 2015 at 18:12
  • $\begingroup$ @EngineerToast Ha ha, LOL. I can't believe it. Working on this puzzle inspired me to use this type of code in one of my puzzles and still I didn't recognize it here!... $\endgroup$
    – BmyGuest
    Jul 26, 2015 at 20:08
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The answer below was valid prior the image-edit. It does no longer apply.

This quite likely is a too simple solution, but two owls stand out: A2 and D7

These two owls are the only ones with a unique eye combination. All others copy at least one other owl.

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  • $\begingroup$ Those are actually the correct owls and an artifact of how I made them different. This has sadly circumvented what was intended to be a clever scheme. I should have used a different method to mess them up which is obvious in hindsight. The only puzzle now is what the social rule is. I'll change those two owls when I get to work but they'll still be the right answer. $\endgroup$
    – Engineer Toast
    Jun 26, 2015 at 10:50
  • $\begingroup$ @EngineerToast Yes, I had a similar problem with my puzzle. It is so hard to find a patter which does not at the same time fulfil a simpler rule. I'm working on the rule. (Well, not now as I have to work, but later.) $\endgroup$
    – BmyGuest
    Jun 26, 2015 at 10:52
  • $\begingroup$ @EngineerToast Well, the "easy" social rule is of course: "Every owl has to copy at least one other form the parliament." $\endgroup$
    – BmyGuest
    Jun 26, 2015 at 10:53
  • $\begingroup$ +1 for a perfectly valid find. I still updated the picture and changed their eyes so this doesn't apply any more. $\endgroup$
    – Engineer Toast
    Jun 26, 2015 at 12:10
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I'm still struggling to see this, but I want to get some momentum into this puzzle, so as work in progress I'm summarizing some ideas.

First the facts (approved by the OP.):

  • The odd-one-out owls are A2 and D7
  • Only 30 eye-combos are valid (whatever valid means)
  • The pattern does not rely on the fact, that it's a 9 x 9 grid or a total of 81 owls.

Then some observations:

  • There are only 18 distinct combos visible
  • There isn't a single double-combo with both eyes looking the same direction
  • Occurring combos appear between 2 and 9 times and the histogram is not very distinctive.
  • It is maybe easier to analyse the image by taking out the owls and representing unique eye-pairs by a single colour.

Easier

Some ideas to work on:

- The fact that the "wrong" owls were replaced without altering the other pattern, or indeed the fact that the patterns exists with some mistakes in it, lets one assume that the pattern does not depend on the other owls, except the dependency is such, that both incorrect owls depend only on each other and no other depends on them. This rules out things like "left neighbour" or "sum of the row" etc.

- The fact that there are invalid combos needs analysing. What logic reason can reduce 64 --> 30 ? Some non-decimal number system maybe?
- Is it a 2D or just a 1D pattern? If 1D, what is the "sequence" order? left-right or up-down?

- Are all owls determined by a rule, or is there a "seeding" owl which defines the pattern. From the storyline, all owls should "independently" be able to match a pattern.

- It is intriguing that - if you just read the lines left-right and continue to the next line - you find some of the patterns repeat themselves. This is most noticeable in the blue-purple-pink sections. Sometime patterns repeat for longer than others, but I can not think why exactly they break differently. Obviously it has to do with "other owls", but how?

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    $\begingroup$ It's certainly nice to know the time I put it to align those friggin' irises hasn't been ignored. I can confirm and add a few things as a token of appreciation: The pattern does not rely on a relationship with all the other owls but it does rely on all the owls earlier in the sequence (If an owl leaves, all the owls after it will change). Owl #1 is A1 and Owl #2 is B1. The two odd owls (A2, D7) stood out in the original image because the eye combinations I gave them when I made them wrong were both invalid combinations. $\endgroup$
    – Engineer Toast
    Jun 30, 2015 at 17:41
  • $\begingroup$ Oh, and here's one more: Technically speaking, one of the 30 valid eye combinations can only be properly represented by an animated image. $\endgroup$
    – Engineer Toast
    Jun 30, 2015 at 17:44
  • $\begingroup$ Thanks for that. So the important thing to figure out now is, is it a 1D sequence where A2 is just following B9 (which I believe would be a bit fiendish) or if it restarts at A2. Oh, and I have indirectly gotten an additional hint by you "replacing" the other owls ;c) $\endgroup$
    – BmyGuest
    Jun 30, 2015 at 19:16
  • $\begingroup$ I believe the solution is simpler than you are expecting. The only mathematical concept that might help you would be the unit circle. At least, that's what I used to make sure my construction was accurate. No addition, subtraction, factorials, up-arrow notation, or Fourier transforms required. $\endgroup$
    – Engineer Toast
    Jun 30, 2015 at 19:34
  • $\begingroup$ So many hints and I still don't see it. I'm pretty sure I'll bite myself once I see the solution ;c) $\endgroup$
    – BmyGuest
    Jun 30, 2015 at 19:49
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Is it...

the ones at (1,1) and (0,2) where the bottom left one is (0,0)? They're the only ones looking at each other directly.

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    $\begingroup$ Using your schema, the owls at (4,0) and (5,0) are also looking directly at each other. (I just numbered the picture. I'm referring to A4 & A5.) $\endgroup$
    – Engineer Toast
    Jun 25, 2015 at 20:39
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The rule is that..

an owl may only make eye contact with at most one other owl. Owls are making eye contact if they are looking in each others direction with at least one eye and there are no other owls between them.

The two owls breaking this rule are...

b9 and c9 who are looking at each other as well as c9 and b8 who are looking back at them.

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  • $\begingroup$ H7 is making eye contact with both G6 and H6 (phew I thought you had found another applicable rule) $\endgroup$
    – Engineer Toast
    Jun 26, 2015 at 12:05
  • $\begingroup$ Oh so he is! And though I had marked every owl looking at another. At least I haven't broken your puzzle :D $\endgroup$
    – Bob
    Jun 26, 2015 at 12:18

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