One quiz at a time

[AW77]

Well, if my old mathematics teacher could know this. I was really bad at mathematics. I always had a kind of gentleman's agreement with her: I'm always present and smiling at her, for this I would get a D

PS: It seems that I'm still bad at mathematics.

[jdaw1]

After the new arrangement I still think the pattern is the same.
Now the two forms are:
1st line, 1st from left
5th line, 2nd from left

Not only wrong, but profoundly unsatisfactory. An ugly suggestion. When you have it, you will really know it. When you have it, you will think the puzzle elegant and simple even if it took you ages to get.

I'd go for the two circles in circles (as the only images with no vertices)

Ditto.

Does the white "square" (space) constitute part of each image?

No, it is the background, and the same for all of them.

[jdaw1]

Now my question is:
What is my favourite !

Not your question. Ignore Daniel.

[jdaw1]

There follow twenty small images. Eighteen have something in common. The other two do not have the quality of the eighteen, but do have a different quality, for both of the two this quality being the same but not that of the eighteen. Which two are different, and why?

To prevent information being imagined where there is none, the order of presentation is random.







Perhaps those starting a new page could quote this whole post.

[jdaw1]

However, I doubt that "multiple shapes" and "single shape" are the qualities that Julian is looking for.

The betting money has you as the favourite to get this.

[jdaw1]

There is an easy observation that provides a key.

[jdaw1]

Just to emphasise that there isn’t trickery about minor drawing differences, the puzzle is also available in PDF.

[Glenn E.]

However, I doubt that "multiple shapes" and "single shape" are the qualities that Julian is looking for.

The betting money has you as the favourite to get this.

Interesting. I would have bet on Daniel. So if true, it is likely only because Phil isn't here.

So far I'm not finding any satisfactory answers. Lots of common qualities, but none (so far) that leave exactly 2 out.

[djewesbury]

This is one of these questions that's about a mental trick, or sleight of hand, of some sort. In some subtle way this is not really about shapes and shading.. This is not a 'spot the difference'.. It's about number.

[RAYC]

Still not sure i understand why my answer - or AW77's answer - was "wrong" (as opposed to "correct, but not the differentiating qualities i was looking for")

[djewesbury]

It reminds me of this...
..apparently this contains a message but I never worked out what it is.. (and besides, they didn't spell out whole words with signal flags, they used a number code.)

[djewesbury]

We have been invited to make observations - easy ones at that.

Octagons have twice as many sides as squares; squares have four sides, circles have one.

(I doubt we are counting sides.)

There are at least three different shades used.

Anyone else observe anything?

[djewesbury]

Is it to do with planes of symmetry?

[Glenn E.]

Anyone else observe anything?

Circles are light, octagons are medium, squares are dark. Regardless of size.

No image uses all 3 shapes or shades.

4,3 and 2,4 are the only images that use 2 octagons.

There is only 1 small octagon.

It isn't octal encoding.

[PhilW]

Best guess at the moment: (1,3) and (2,1) are a unique pair in that they have infinite rotational symmetries, while the rest do not.
(however, I have a feeling that the answer being looked for is somewhat more subtle than this)

Observations:
All images contain 1-3 objects.
Each object has one of three shapes (with sides=1,4 or 8) [or one of 4 shapes, if "none"/not present is considered as a valid value].
Each object is always filled with the same colour/shade.
Each object may be one of three sizes (small, medium, large).
There are 20 unique images.
Every image contains a small object.
The only images containing only 1 object (ignoring "none" shape type) contain a small object.
No image contains more than 2 objects of the same shape (and hence colour since shape-to-colour is a 1:1 mapping).
No image contains all three object types.
Images counts for small objects: none=0, circle=10, square=9, octagon=1
Images counts for medium objects: none=5, circle=5, square=5, octagon=5
Images counts for large objects: none=6, circle=6, square=4, octagon=4

btw: good question as long as it has a good answer of course!

[djewesbury]

(.... clears throat....)
Any clues on observations so far?

[Glenn E.]

I think we're going about it the wrong way. We're looking for the two exceptions, when we should be looking for the common rule. The common rule will be the elegant solution, at which point the two exceptions will be obvious.

[djewesbury]

I think we're going about it the wrong way. We're looking for the two exceptions, when we should be looking for the common rule. The common rule will be the elegant solution, at which point the two exceptions will be obvious.

Yes, quite. *nods authoritatively*

[jdaw1]

btw: good question as long as it has a good answer of course!

It has a good answer.

PhilW and Glenn E. are almost close.

[RAYC]

Still not sure i understand why my answer - or AW77's answer - was "wrong" (as opposed to "correct, but not the differentiating qualities i was looking for")

Please comment. Why are the most obvious answers (that fulfil the criteria provided) "wrong"?

If they are inelegant, that is (in my opinion) the fault of the question (for not excluding their possibility)

[jdaw1]

Please comment. Why are the most obvious answers (that fulfil the criteria provided) "wrong"?

First, and this is sufficient, because the question master says that they are wrong.

Second, also because there are many possible answers of that sophistication, of that elegance, which are neither more not less plausible. So if that is the required standard of usage of information there might be a technical term using the word ‘entropy’ then almost any answer can be deemed correct.
• ‟Because they are the corner answers on the leading diagonal.”
• ‟Because they are the corner answers on the other diagonal.”
• ‟Because they are the first two answers.”
• ‟Because they are the last two answers.”
• ‟Because they are the middle two answers.”
• ‟Because they are the lightest two answers.”
• ‟Because they are the darkest two answers.”
• ‟Because they are the two answers of middling light absorbance.”
• ‟Because they are the smallest two of the monochrome answers.”
• ‟Because they are the largest two of the monochrome answers.”
Etc, ad irrelevant infinitum.

Whereas the correct answer so elegantly uses the available information that it is self-evidently the, rather than ‟a”, correct answer.

[RAYC]

Second, also because there are many possible answers of that sophistication, of that elegance, which are neither more not less plausible. So if that is the required standard of usage of information there might be a technical term using the word ‘entropy’ then almost any answer can be deemed correct.
• ‟Because they are the corner answers on the leading diagonal.”
• ‟Because they are the corner answers on the other diagonal.”
• ‟Because they are the first two answers.”
• ‟Because they are the last two answers.”
• ‟Because they are the middle two answers.”

Forgive me if i am being dim, but all of these would have been excluded by your intial instructions (whereby order is not important)?

‟Because they are the lightest two answers.”
• ‟Because they are the darkest two answers.”
• ‟Because they are the two answers of middling light absorbance.”
• ‟Because they are the smallest two of the monochrome answers.”
• ‟Because they are the largest two of the monochrome answers.”

These do not, in the same way as the answers previously suggested, explain two qualities or characteristics that set 18 symbols apart (on the one hand) from the other two. They are a qualitatively different type of answer - i would go as far as adopting the favoured guardian reposte of "stawman argument"

[djewesbury]

In the red corner....

[Glenn E.]

‟Because they are the lightest two answers.”
• ‟Because they are the darkest two answers.”
• ‟Because they are the two answers of middling light absorbance.”
• ‟Because they are the smallest two of the monochrome answers.”
• ‟Because they are the largest two of the monochrome answers.”

These do not, in the same way as the answers previously suggested, explain two qualities or characteristics that set 18 symbols apart (on the one hand) from the other two. They are a qualitatively different type of answer - i would go as far as adopting the favoured guardian reposte of "stawman argument"

Actually, I see these answers as very similar to the two that Julian ruled insufficiently elegant. These all identify the 2 without providing an elegant similarity for the 18. "Each image contains multiple shapes" is an inelegant grouping. It is true, except for the 2, but it isn't an answer worthy of a puzzle.

We have yet to identify the common quality that the 18 share. We keep saying "these 2 are different in this way" without really saying "these 18 are similar in this other way," other than to reverse the first.

I also believe that the quality that the 2 share is different than the quality that the 18 share. Not just the opposite of the quality that the 18 share, but actually a different quality.

[jdaw1]

both forms do only have one line and simply white space around them

the two circles in circles (as the only images with no vertices)

Are there other answers equally plausible?

Images counts for small objects: none=0, circle=10, square=9, octagon=1

So octagons must be special (as indeed they are, a bit, but not as special as all that), in which case the two with maximum number of octagons (for there are only two).




Or, different reasoning leading to the same answer, there are two with two octagons. Interesting. But there are four with two squares:

And there are seven with two circles

So, given that the answer has two oddities, it can only be the octagon majority:

(But this is unsatisfactory: the oddities are only the oddities in the context of this question, rather than a more absolute oddness.)



Or the largest two using only shape? (That is, the only two comprising more than one shape, all used shapes being equal.)


And maybe I can concoct other equally plausible non-answers. No. The correct answer, when understood, will very clearly be the correct answer, and there can be no other.

[jdaw1]

There follow twenty small images. Eighteen have something in common. The other two do not have the quality of the eighteen, but do have a different quality, for both of the two this quality being the same but not that of the eighteen. Which two are different, and why?

To prevent information being imagined where there is none, the order of presentation is random.







Perhaps those starting a new page could quote this whole post.

[djewesbury]

From what Julian has already said, I think that Glenn is absolutely correct here. But, as much as I've been staring at this puzzle for the last two days, I can't get beyond numbers of sides, or numbers of vertices, or some sort of abstruse and inelegant combination such as [shade + vertices]. And I feel very strongly that these are all wrong. Which is why I thought it was about symmetry. Then I thought they were all some kind of section of polygonal shapes, but that led me nowhere. Then I tried considering negative space. Then I got a migraine.

[jdaw1]

From what Julian has already said, I think that Glenn is absolutely correct here. But, as much as I've been staring at this puzzle for the last two days, I can't get beyond numbers of sides, or numbers of vertices, or some sort of abstruse and inelegant combination such as [shade + vertices]. And I feel very strongly that these are all wrong. Which is why I thought it was about symmetry. Then I thought they were all some kind of section of polygonal shapes, but that led me nowhere. Then I tried considering negative space. Then I got a migraine.

All wrong, most especially the migraine (and excepting the ‟I feel very strongly that these are all wrong”). Something very close to the correct understanding has been mentioned, but not by you.

[djewesbury]

No image contains all three object types.

Is this significant..?

[djewesbury]

Oh I know, two of them are vowels.

[djewesbury]

I think a clue would be fair.

[jdaw1]

I could have made the puzzle bigger, including all the appropriate drawings with ≤4 shapes, most of the included drawings sharing the quality of the eighteen, but a few sharing the quality of the two. If I had done so, twelve would have contained all three shapes.

Which won’t help you.

[djewesbury]

... Glenn..?

[jdaw1]

I think a clue would be fair.

Something very close to the correct understanding has been mentioned, but not by you.

These puzzles are never about the answer. They are about the understanding, from which the answer generally follows trivially. It is like happiness. If you seek happiness, you will fail. If you seek understanding, you will find happiness.

[djewesbury]

If you seek happiness, you will fail. If you seek understanding, you will find happiness.

I have to go and lie down...

EDIT: I am only seeking understanding. I only ever seek understanding. I am kneeling and beseeching these picture to give me understanding. But I am not understanding.

[RAYC]

both forms do only have one line and simply white space around them

the two circles in circles (as the only images with no vertices)

Are there other answers equally plausible?

Images counts for small objects: none=0, circle=10, square=9, octagon=1

So octagons must be special (as indeed they are, a bit, but not as special as all that), in which case the two with maximum number of octagons (for there are only two).

This explains why these two are unique, but not what the other 18 have in common. Contrast with the example of the two circles in circles: the quality unique to the 18 is that of vertices. The quality unique to the other 2 is - in the words of Phil - infinite rotational symmetry. Your posited examples do not display this duality - only a one-sided "uniqueness"

[jdaw1]

There is an answer that, when found, is elegant and self-evidently correct. If that isn’t enough for you, then instead accept the prerogative of the question master.

[RAYC]

There is an answer that, when found, is elegant and self-evidently correct. If that isn’t enough for you, then instead accept the prerogative of the question master.

I remain of the opinion - not yet countered - that it is a flawed question if the self-evident answers which fulfil the criteria of the question are "wrong"

[jdaw1]

Or the largest two using only shape? (That is, the only two comprising more than one shape, all used shapes being equal.)

Sorry, a ‟one” went missing. I meant ‟Or the largest two using only one shape?”.

[jdaw1]

I am only seeking understanding.

When the answer is found, that will be known to the finder. The finder could post a complete explanation. Or the finder could post the answer the two images and a cryptic hint, demonstrating to me that this wasn’t a wild guess, but explaining nothing to anybody else. (There is a nice wording that would do just that.) Obviously the latter would allow the non-finders who really ought to get it a little more time to understand. Finder’s prerogative. (Though an explanation would have to follow eventually.)

[djewesbury]

There is an easy observation that provides a key.

Should we revisit this?

[Glenn E.]

There is an easy observation that provides a key.

Should we revisit this?

That's what I've been trying to do, but I'm apparently not very observant.

[djewesbury]

There is an easy observation that provides a key.

Should we revisit this?

That's what I've been trying to do, but I'm apparently not very observant.

Here's an observation. I've been trying to find the link between the 18 pictures that have a link; and the problem is that nos. 1 & 18 are very difficult to connect to the others. And yet they are NOT the two that have something in common with each other and not the other 18. This is a paradox.

[djewesbury]

Observation.
The number of shapes depicted in each picture is equal to the number of colours / shades used.
(This is not the same, quite as Phil's observation earlier.)
Please point out that this is irrelevant.

[jdaw1]

Observation.
The number of shapes depicted in each picture is equal to the number of colours / shades used.
(This is not the same, quite as Phil's observation earlier.)
Please point out that this is irrelevant.

I think it is the same as Phil’s observation. Certainly all circles have the same pale grey, all octagons the same medium grey, and squares the same dark(est) grey. It is of marginal relevance: it shows that it suffices to consider shapes, or greys, according to one’s taste, but having considered one there’s no additional information in considering the other.

[jdaw1]

Clue:

There is an easy observation that provides a key.

Images counts for small objects: none=0, circle=10, square=9, octagon=1

I could have made the puzzle bigger, including all the appropriate drawings with ≤4 shapes, most of the included drawings sharing the quality of the eighteen, but a few sharing the quality of the two. If I had done so, twelve would have contained all three shapes.

If the puzzle had been extended, however far, every innermost shape would be a circle or a square (excepting the one solo octagon already shown).

[djewesbury]

Is this a notation of a counting system? Glenn dismissed octal; is there some other base that would give a key?

[djewesbury]

Does [octagon] = 0? Is this somehow a representation of base 2?

[jdaw1]

You are within reach. So nearly there.

[jdaw1]

There follow twenty small images. Eighteen have something in common. The other two do not have the quality of the eighteen, but do have a different quality, for both of the two this quality being the same but not that of the eighteen. Which two are different, and why?

To prevent information being imagined where there is none, the order of presentation is random.







Perhaps those starting a new page could quote this whole post.