Which square doesn't belong here and why?

Which square doesn't belong here and why?

• I am fine with downvotes. Would appreciate to know the reason so that I could improve the quality of my questions. – Lazy Ninja Nov 28 '14 at 8:57
• I think this question is original and there is no need to be down-voted. But there are guys who downvotes questions like guessing the next in the sequence and find the odd one out puzzles, claiming that it can have multiple correct answers. – AeJey Nov 28 '14 at 9:02
• Downvotes are community indicators for bad quality, a comment is essential only if there is a specific reason, its my downvote and I believe such questions don't contribute to "quality" content in this site - trivial, unsearchable, too broad are some of the reasons – skv Nov 28 '14 at 9:05
• @thin I'm not trying to pressure him into it I'm just trying to notify him we're still here through a comment. It's approaches 24 hours, he's got 7 answers, I'm interested to know which is correct. – warspyking Nov 29 '14 at 9:23
• The reason to consider this question as too broad is because of this very reason that we have many seemingly equally valid and acceptable answers I dont know why its not earning one more close vote – skv Nov 29 '14 at 12:51

3 (third square)

In all the other squares except

3rd square, 3 (three) lines divides the square in to 5 parts, while in 3rd square the lines (three lines) divides it to 6.

The big orange one. All the others are brown.

It's clearly the odd one out.

• This wasn't tagged lateral thinking... – warspyking Nov 28 '14 at 16:32
• It asks which square is the odd one out. I see 5 squares, one of them is markedly different from the others. – Richard Nov 28 '14 at 16:37
• By this logic I can say my screen is the odd one out -_- – warspyking Nov 28 '14 at 17:00
• @warspyking you have a square screen? how peculiar! – njzk2 Nov 28 '14 at 17:58
• @ir7 - The numbers are purely to distract you. – Richard Nov 28 '14 at 23:48

Only number 1...

has lines that meet the bounding square at a corner

Only number 2...

lacks any lines that slant down and to the right

Only number 3...

(a) divides the square into 6 areas instead of 5, (b) contains two complete intersections, and (c) includes a complete red triangle

Only number 4...

has no uniquely distinguishing characteristics. So my guess is 4.

• 4 does have a unique distinguishing characteristic now! The fact that it don't have the others! – warspyking Nov 28 '14 at 16:01
• @warspyking This may be of interest, for both this and countable infinite sets of squares/elements/other things. – hexafraction Nov 28 '14 at 16:57
• @hexa That is interesting... – warspyking Nov 28 '14 at 17:04
• This was my guess. The only one that I thought of at least. – erdekhayser Nov 29 '14 at 13:46
• 4 is the only one who's triangle does not have two sides of the same length. – Michael Dorst Nov 29 '14 at 19:51

3

Because

1, 2 and 4

could be a part of representation of

number 4, mirrored or rotated.

But the picture in number

3

is different.

• how is it different ? it is still 3 lines intersecting. – njzk2 Nov 28 '14 at 14:42
• This is what I thought at first too. – Joe Z. Nov 28 '14 at 16:19
• @njzk2, but they did not across throw their intersection. in those 3 lines ended in proper place – Rafe Nov 28 '14 at 17:48
• @Rafe: sorry I don't understand what you mean by they did not across throw their intersection. 3 lines in a plane either intersect, or 2 of them are parallel. (no figure shows parallel lines, so.) – njzk2 Nov 28 '14 at 18:00
• @njzk2, my bad! not good in english :-) i mean lines in 3rd square continued after their intersection. this is something more that a 4. so 3rd square cannot represent number 4's shape. but you can create number 4 with continuing lines of other squares. – Rafe Nov 28 '14 at 18:08

I choose

frame 3 because is the only one that shows the triangle created by the three lines through their pairwise intersections. In all four cases the (non-trivial) triangle exists, but in cases 1, 2 and 4 it is not presented within respective frame. (Edit: note that this is technically equivalent to AeJey's answer that observes the number of parts the frame is split into by the three lines.)

Clearly the odd one out is

4.

Graphical explanation

Wordy explanation:

1,3,2 are slices of a bigger picture. 4 does not fit with any of them. Even if we prolongue the lines in 1,2,3 they still fit well in the overall picture.

• I'm sorry, but I don't understand. What are you saying? – Michael Dorst Nov 29 '14 at 19:53
• @anthropomorphic Perhaps it makes more sense now? – Tibos Nov 30 '14 at 9:01
• I get what you're saying, but I don't think you're right. I think you could still find a rotation of 4 that would fit in the picture. Also, 1 and 3 don't match up that well. – Michael Dorst Nov 30 '14 at 21:03

Frame 3

For three reasons:

• 1

When you extend the lines of 1, 2, and 4, they can join in a path of 3 lines which are in broken. You cannot do this with 3.

• 2

When you look at how many sections of white space there are in 1, 2, and 4 there's 5. In 3 there's 6

• 3

3 is the only square, where the lines within the frame make a triangle.

So obviously it has to be the answer stated above!

• I was going to answer three for your reason 1. – Chris Nov 28 '14 at 16:37
• And only 3 shows 2 intersections. – Florian F Dec 1 '14 at 14:26