enter image description here

Which image (1-5) could replace the blank tile?



Neighbours are important




The lines


Two at a time...

Big one.

Criss crossing lines after overlapping each pair of images

  • $\begingroup$ Sorry for my bad drawing with the numbers $\endgroup$ Oct 10 '16 at 16:00
  • $\begingroup$ Is this a sequence, a set that satisfies a property, or do you not want to say? $\endgroup$ Oct 10 '16 at 16:08
  • $\begingroup$ @greenturtle3141, I'll say this, you can't just look at individual tiles to work out the answer $\endgroup$ Oct 10 '16 at 16:09
  • $\begingroup$ Add more hints! $\endgroup$
    – bill bsl
    Oct 11 '16 at 18:58
  • 1
    $\begingroup$ I first thing I did was to try overlapping... But nu :c $\endgroup$ Oct 13 '16 at 22:29

Image 4, because of two observations:
- within a single image, there are no crossed lines (T's are okay)
- in all pairwise overlaps, no line in one image is crossed twice by the other image

Image 4 is the only option that meets both criteria. (3 and 5 cross themselves, and 1, 2, 3 cause double-crossings in the overlap.)

  • $\begingroup$ ...I can rest at peace... Well done! I'll award the bounty soon, but for now enjoy the accept! $\endgroup$ Oct 17 '16 at 20:43
  • 1
    $\begingroup$ "T's are okay" - Well, all intersection angles are okay, just not an intersection that appears to be a pass-through. $\endgroup$
    – John
    Oct 17 '16 at 21:56
  • $\begingroup$ @John Yes, that is what I meant. 'T' was the most concise way to express that. The focus is less on the specific angle, and more on the fact that the lines touch, but do not cross. I could have used 'Y', but 'T' is already used to describe topology (e.g. road intersections). $\endgroup$
    – Phlarx
    Oct 17 '16 at 22:06
  • $\begingroup$ @Phlarx, I know you knew. Just clarifying for example that possible solution 5 is not say, a down arrow pointed at a right angle, but that it's specifically a 'cross' with a line going up. Good job by the way!! +1. $\endgroup$
    – John
    Oct 17 '16 at 22:11

Since the hints seem to point to

pairwise overlaps, here's a diagram to show what that looks like. Still don't know what the answer is, though.

enter image description here

  • $\begingroup$ That is a very good start! Just what I was looking for. Now check the other hints... $\endgroup$ Oct 17 '16 at 18:35
  • $\begingroup$ The big hint wants intersections... Is it not that each line in one picture intersects another in the second? Because it doesn't work for the first and last two... $\endgroup$ Oct 17 '16 at 18:40
  • $\begingroup$ @greenturtle3141 Yeah, it did seem like that would be possible except for the first and last pairs. $\endgroup$ Oct 17 '16 at 18:43
  • $\begingroup$ @greenturtle3141 It almost looks like at least one intersection location is preserved in each successive pair, except for the last one. $\endgroup$ Oct 17 '16 at 18:48
  • $\begingroup$ Intersection location preservation seems almost correct except for that last pair. $\endgroup$ Oct 17 '16 at 18:50

4. The result of the ex-triangle is a side rearrangement. Only 4 complies with that. Then sides get to multiply and reduce until they get to another triangle.

  • $\begingroup$ Afraid not good effort though $\endgroup$ Oct 11 '16 at 10:33
  • 3
    $\begingroup$ I don't get what you mean in your answer. $\endgroup$ Oct 11 '16 at 11:25
  • $\begingroup$ There is no simpler rule than this one. $\endgroup$
    – Overmind
    Oct 12 '16 at 4:47
  • 2
    $\begingroup$ If it's so simple can you please clarify your answer? What and where is this extriangle? $\endgroup$ Oct 13 '16 at 22:36
  • 1
    $\begingroup$ What is X and the other letters... What do you mean by line rearrangement... What do you mean by first R... You really need to explain as if I'm an idiot and use pictures because I'm not getting the logic here. $\endgroup$ Oct 14 '16 at 18:41

My Guess,

My Answer is 5.
Above Totally 9 Images, So I splited into 3 section.
3rd image have 3 lines,
6th image have 4 lines and
so, 9th image(blank) should have 5 lines.
Answer Option Images Have only one Five Line Image that is 5th image.so, MY Answer is 5 image could replace blank(9th) one.

  • $\begingroup$ Sorry nice try, but afraid not $\endgroup$ Oct 11 '16 at 16:26
  • $\begingroup$ This doesn't make any sense to me.  Would you care to explain your answer in clear language? $\endgroup$ Oct 14 '16 at 3:32

I think it's:

1. Because there are multiple reflections, especially given the last clue. I can't figure the reasoning, but early on I saw that 6 & 7 merged resulted in a common copy icon. After overlapping and tilting 3 & 4, there's a double X shape. That leaves 1, 2, & 5 orphaned in this explanation.

  • $\begingroup$ I'm afraid that was just a coincidence... nice try though $\endgroup$ Oct 17 '16 at 16:05
  • $\begingroup$ @BeastlyGerbil, Wahh... wahhh... (sad horn)... I'll take another look later. $\endgroup$
    – John
    Oct 17 '16 at 16:08

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