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Hi I saw this sequence and cant's stop thinking about it.

sequence

I was guessing that the number of thick-walled dots represents the number of sides for the next shape in the sequence

the 3rd shape has 3 thick-walled dots, and the 4th has 3 sides

the 4th has 6 dots, and the 5th could be said to have 6 sides (though that's a stretch.....)

and maybe a rounded box is considered to have 0 sides?

It just seems that there must be a better explanation, and maybe a whole different answer.

EDIT

I had a new idea, that still feels like a stretch

The solution would be the second figure if we dismiss any relationship between the number of dots and just focus of the shape that the thick-walled dots create.

the 4th makes a rectangle and the next figure is a rectangle. the 3rd makes a triangle and the next figure is a triangle. the 2nd of the options makes some weird shape that might resemble the 3rd, and here starts the stretch I was talking about. finally the 1st does not have a shape with means the next should not have side defined shape and since it has no corners it does not have a side.

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    $\begingroup$ Where's it from? (An IQ test of some sort? A puzzle hunt somewhere?) $\endgroup$ – Gareth McCaughan Dec 5 '17 at 2:51
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    $\begingroup$ Some tests like this do not have a specific solution, but a (more or less) consistent explanation to a proposed solution is the key part then. $\endgroup$ – Ctx Dec 5 '17 at 11:04
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    $\begingroup$ Hm, your explanation would be more consistent when you talked about "corners" instead of "sides". However, I do not see how the fifth figure could be interpreted having 6 sides (or corners) $\endgroup$ – Ctx Dec 5 '17 at 11:14
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    $\begingroup$ Some shapes look like they have thicker borders. This could be relevant. $\endgroup$ – J. Siebeneichler Dec 5 '17 at 13:11
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    $\begingroup$ It could be that having more dark circles than light ones means the next shape has a thick border, but that’s not saying much by itself when you have two relationships to go on. $\endgroup$ – Ry- Dec 5 '17 at 14:46
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At first I thought that

the thick-walled dots may represent the shape of the following figure. That would mean, that number 2 is the solution, but it has one dot at the top that does not fit the shape.

I then tried to find a pattern in the numbers, but I wasn't able to find one. But here are the numbers (I wasn't able to make it a spoiler):

\begin{array}{|c|r|r|r|r|r|} \hline \textrm{figure}&1&2&3&4&5 \\ \hline \textrm{sides}&4&?&7&3&4\\ \hline \textrm{“white" dots}&25&?&7&3&1\\ \hline \textrm{“black" dots}&0&?&3&6&9\\ \hline \textrm{dots}&25&?&10&9&10\\ \hline \end{array}

I could not get to a solution, but maybe someone can use my work...

A search on OEIS

for patterns in the white dots concluded that there are only number sequences for 1, 3, 7, 15, 25 and none if swapping the 15 with 18 or 22. This leaves the fourth figure as the answer. Link to OEIS search.

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  • $\begingroup$ I did a similar breakdown. Only pattern I could see was that the "black" dots can be made to follow a fibonacci-esque pattern with a 3 in the blank. $\endgroup$ – Alconja Dec 5 '17 at 12:28
  • $\begingroup$ Thought about the same thing, that would only leave figure 1, 3 or 5 as the solution. I also thought the "white" dots could be substracted by 10, 8, 4, 2, forming a -2 /2pattern, but that is a bit of a stretch and would leave figure 4 as the solution $\endgroup$ – Luca H Dec 5 '17 at 12:32
  • $\begingroup$ @Alconja I added something, but that clashes with your fibonacci approach. You can find 0, 6, 3, 6, 9 in several decimal expansions, but that is a veeeery big stretch. $\endgroup$ – Luca H Dec 5 '17 at 12:44

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