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I'm reading up on various IQ tests, and a slideshow that I stumbled upon gave the following example:

Question

This doesn't make sense to me, as none of the options duplicate the conditions in the far left image, and it's left me thinking that it's simply a mistake in the slideshow. That seems unlikely though, so thought I'd see if you guys can explain where my logic is falling apart, as there's a bunch of bright folk around here.

Link to the original source https://www.slideshare.net/CLARENCEAPOSTOL1/cfit-test-62617085

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    $\begingroup$ This makes no sense to me either. I guess, don't trust everything you read on the internet. $\endgroup$
    – greenturtle3141
    Jul 25, 2017 at 17:35
  • $\begingroup$ Yeah that could be the simple explanation, it was a legit seeming presentation on LinkedIn, so perhaps I gave it more credit than it deserved. We'll see if anyone can crack the riddle though, we could both be mistaken! $\endgroup$
    – Callum Bradbury
    Jul 25, 2017 at 17:36
  • $\begingroup$ 3 and 5 are topologically identical, so it must be a mistake. Can you provide the source? $\endgroup$
    – Dr Xorile
    Jul 25, 2017 at 17:47
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    $\begingroup$ This is quite possibly the worst question I have ever seen. What's the IQ of the people who made it? Jeez. $\endgroup$
    – Arthur Dent
    Jul 25, 2017 at 19:28
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    $\begingroup$ "which one duplicates the conditions in the first box" - it's the closest, only difference is the lacking of square crossing, and the dot doesn't care about that (as far as I can understand it) $\endgroup$
    – Stephen S
    Jul 25, 2017 at 20:07

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The explanation in the slide seemed very odd, so I Google Image searched "culture fair IQ topology" and lots of variations of this image came up:

If you look at the topology question, it matches the explanation perfectly: we need a dot inside the circle but outside the square, making the only possibility choice #3.

So I think that at least the explanation is not for the puzzle given. As to the puzzle given, I also do not see a solution that matches the configuration of the first picture...

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    $\begingroup$ Wow, nice find. This is the most plausible answer yet, although it begs the question 'what on earth was the answer to the image provided?' $\endgroup$
    – Callum Bradbury
    Jul 25, 2017 at 20:55
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    $\begingroup$ My best guess, based on Dr Xorile's comment that 1 and 4 are topologically identical, was that in one of those the squares were meant to overlap and not only touch, giving a possible solution. I'm not completely sure about that speculation, though. $\endgroup$
    – ffao
    Jul 25, 2017 at 21:07
  • $\begingroup$ I think I figured it out, and have posted as an answer - interested in your opinion on my solution $\endgroup$
    – Callum Bradbury
    Jul 25, 2017 at 21:19
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I believe ffao is correct about the image being a mistake, however we're then left with 'what is the solution to the original image?'

I think I figured it out...

enter image description here

Misdirection, making us assume image 1 has two squares in it, when it's actually two L shaped pieces.

Thoughts?

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  • $\begingroup$ This answer seems to me to be the only logical explanation. $\endgroup$
    – Petr
    Jul 26, 2017 at 13:25
  • $\begingroup$ I think you are correct about the diagram choice, but "no" there is not a 3rd shape being introduced. I also think the dot would be placed in the center of the intersection of the two boxes. In all diagrams, the circle can take a dot, but in no other diagrams do the two squares intersect without one being subsumed. $\endgroup$
    – Yorik
    Jul 26, 2017 at 16:41
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    $\begingroup$ But it would not be 'as in the one on the left' if the dot was not within the circle, so I don't see how what you're saying could be the answer $\endgroup$
    – Callum Bradbury
    Jul 26, 2017 at 17:08
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Most likely:

There has been a mistake.

Oh, the irony...

There are several things wrong here:

Grammatical errors:

  1. It says '5 choices provided' and there are 6, if we assume that the box furthest to the left is part of the options.
  2. Says 'the box' and there are 2 boxes in each

Logical errors:

       Scenario 1:

  • If the box furthest to the left is the one we are supposed to duplicate conditions as the question says, then not only does 3 not fit, but none of them do.

       Scenario 2:

  • If we go with the example and have to find a box in which it is possible to place a dot inside a circle but outside the box(es), then the middle four (or first four excluding the leftmost one) all work.

So there is no answer either way...

My guess as to what happened is that the writer linked the wrong image or the leftmost image is missing.

Don't worry, it's not you - there is definitely a mistake somewhere.

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    $\begingroup$ The one on the far left isn't a choice, it's the example which you're supposed to use to 'match' one of the other 5. As to 'the box', I do agree that hints at some sort of mistake being made, but can't say for sure. $\endgroup$
    – Callum Bradbury
    Jul 25, 2017 at 20:32
  • $\begingroup$ I concede that there are missteps with their wording, but i still think the directions are clear. As Callum stated in a comment under my answer, it is difficult to decipher where the question is and the explanation begins. $\endgroup$
    – Jason V
    Jul 25, 2017 at 20:54
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    $\begingroup$ This is the correct answer, for the following reason: The slide shown in the OP is slide 15 of the linked presentation. Slide 17 describes how the test proctor is supposed to give instructions, and directly contradicts the hint on slide 15: "In the separate square of the first example, there is dot which is in both the circle and the square. Now look at the five possible answers and see if you can find a drawing where you could put in one dot that will be inside both the circle and square." [emphasis mine] $\endgroup$
    – shoover
    Jul 25, 2017 at 22:42
  • $\begingroup$ @shoover interesting find. There is definitely something wrong here... $\endgroup$
    – Beastly Gerbil
    Jul 26, 2017 at 14:30
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This has a very logical explanation. You must follow the example in the left most box as to where to place the dot in the subsequent examples

The dot must fall inside a circle, and outside of the box

the topology is ONLY for the dot- as that is all that is stated. Don't get hung up on superfluous information.

enter image description here

example 1 the dot falls into both boxes- fail

example 2 the dot doesn't fall in either- fail

example 3 the dot falls inside the circle but outside of both boxes- pass

example 4 the dot falls inside both boxes- fail

example 5 the dot is inside of a box, and not the circle- fail

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    $\begingroup$ please excuse my use of ms paint- on a junk laptop. my red points are off just a bit but it should suffice $\endgroup$
    – Jason V
    Jul 25, 2017 at 18:02
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    $\begingroup$ In the left most box, is the dot not inside both boxes? Wouldn't that mean the dot had to be in both boxes in the answer, not outside of both? $\endgroup$
    – Callum Bradbury
    Jul 25, 2017 at 18:03
  • $\begingroup$ it explicitly states "Choose the diagram in which a dot could be placed as in the one on the left" and the instructions state it should land "outside the box but inside the circle" $\endgroup$
    – Jason V
    Jul 25, 2017 at 18:06
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    $\begingroup$ I have conceded that it is a poorly written question, and i look forward to your answer to see how you interpret the question. $\endgroup$
    – Jason V
    Jul 25, 2017 at 19:51
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    $\begingroup$ @Jason I don't think there is a way to interpret the question (see the logistical errors in my answer). I just think there must have been a mistake. $\endgroup$
    – Beastly Gerbil
    Jul 25, 2017 at 20:01
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I agree that the question is unclear — hopelessly unclear and unanswerably cryptic.  As B. Gerbil points out, it isn’t even clear what “option 3” means.  But, if we assume that the six boxy diagrams are numbered 0, 1, 2, 3, 4, and 5 (left to right), or BLANK, 1, 2, 3, 4, and 5 (as in the version that ffao found), and given that “option 3” is the answer, it can be explained as follows:

Pick the boxy diagram (of the rightmost five) which, like the leftmost one, has the property that

both squares are contained entirely within the circle.

In other words, select the figure in which

it is im⁠possible to place a dot that would lie in⁠side a box but out side the circle.

The only way this makes sense is if the dot in diagram 0 is a complete red herring.

If this question were posed here (rather than being cited here), it would be closed as “too broad” or “Off-Topic: This question may invite speculative answers, as the question is not fully defined. …”  It’s possible to construct equally plausible justifications for the other options:

  • option 1: The squares intersect (if only at a single point), and that intersection is contained within the circle.  AND the squares are the same size and are parallel to each other.
  • option 2: The squares overlap (but neither is contained within the other).
  • option 4: The squares intersect (if only at a single point), and that intersection is contained within the circle.  AND the squares are laid out more-or-less left-to-right.
  • option 5: >50% of one square is contained within the other.

I feel troubled by using arguments about sizes, parallelism, and left-to-right layout in a test that’s supposed to be about topology, but the Good Ship Logic has sailed.  And, as others have pointed out, options 1 and 4 are topologically identical.

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It took a while, but I think I have it. They're asking you to assume that those 2D shapes are floating in a 3D space, and that you can move around to look at them from another angle. So, select the shape which can be looked at from a different angle to reproduce the original shape.

  • It can't be the second box: You're staring out looking (nearly) orthogonal through the centre of the circle. If the circle is behind the squares in 2, you could flip the perspective around to make it bigger than the squares. But wiggling the axis so parallax makes the squares overlap would pull them out of the center.
  • It can't be the fourth box. No perspective will make the squares align.
  • It can't be the fifth box. No perspective will make the squares align, and you have most of the problems of the second box too.
  • It probably could be the sixth box (circle far away, small square in between, and large square close up, then look from the other direction), but I think the squares misalign too much. If the border is part of the diagram, six is right out.
  • It must be the third box. Look at the two squares as coplanar, and the cirle as farther away. Then move your perspective to the other side of the circle, looking up out of the page and rotate 90 degrees. You still need to tilt your perspective slightly so the squares are in the center of the circle, but it's little enough that neither the original nor the result is distinguishable from an ellipse anyway.
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If you look at the statement Select the figure in which, it is possible to place a dot that would lie outside the box but inside the circle. So leaving 3rd and 5th, there is possibility that it can be placed in square and circle both. It is not asking specific point where you can place. Question may sound ambiguous but still if you just keep your head clean you can understand it. In 3rd and 5th, wherever you put the point in circle, it will lie outside the box only.

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I am assuming that there is a second set of figures originally given as an example which have been removed, and therefore the second and third sentences of the question can be ignored. The "For example" text bears no resemblance to the image provided at all.

Regarding the first sentence of the question and the image provided, the answer is the third box along, with the two squares intersecting and a circle off to the side. Topologically speaking the aim is to put the dot in a place that satisfies two conditions 1) Within the intersection of two sets. 2) Within another set that wholly encompasses the first two sets.

The trick is that none of the sets are defined, therefore the inside of the circle in the third image is not necessarily the set - the set can just as easily be the space outside the circle, with the circle bounding an area outside of the set.

Placing the dot in the intersection of the two squares in the third image satisfies both constraints.

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This is a question that requires some specific knowledge of the mathematical field of topology. In that field you are allowed to manipulate shapes within certain parameters (primarily, you can't cut/break a shape or create a new hole in a surface, or push shapes through other shapes such that they intersect when they previously didn't). In topology, a coffee mug is equivalent to a doughnut.

The example box has a circle surrounding two adjacent L-shaped polygons, with a dot between the polygons. That means you're looking to place a dot such that it's inside the circle and outside both polygons, with the polygons inside the circle. Box #3 is the only one that satisfies those conditions, though it (through the rules of topology) re-shaped the polygons into squares and moved them apart slightly -- but they're both still contained in the circle and nonintersecting.

In box #1, the circle now intersects the boxes, violating the rules of topology. In box #2, the circle is no longer surrounding the boxes, violating the rules of topology (you can't push a shape through another shape). In box #4, you have another intersection problem (this one is equivalent to box #1). Box #5 has broken a variety of rules, with one box now surrounding the other box and the circle (everything has been pushed through everything).

That leaves box #3 the only topological equivalent to the example.

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You guys, it's pretty simple. It's meant to say "far RIGHT box", not "far LEFT box". From there, the puzzle is simple.

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    $\begingroup$ there isnt a dot in the right one $\endgroup$
    – bleh
    Jul 27, 2017 at 3:31
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I'm sorry for spoiling. The thing is that there is something missing. These 6 squares are actual choce options for the problem that has been cut off. First one (with a dot) is the right answear and the dot is there just to clarify the choice.

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  • $\begingroup$ Hi, welcome to the community! That doesn't make sense, as the text states choice 3 is the correct answer. If the problem was cut off the text would say choice 1 was the correct answer. $\endgroup$
    – Callum Bradbury
    Oct 14, 2018 at 3:20

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