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it comes from http://www.foundalis.com/res/bps/foundal/p162.htm

What you need to do is to distinguish the patterns on both sides, what is the common feature on the left and what is the common feature on the right

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2
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Not sure about the first one, but for the second:

If you count along each grid row by row, then the first group has black squares evenly spaced (5, 6, 4, 7, 2, 9), whereas the second group does not have such even spacing.

Edit: after a bit of googling, it appears that the first one has a couple of possible solutions (taken from a reddit thread):

1) The first group has an equal number of acute angles as non-acute, whilst the second group doesn't.
2) The first group has shapes such that every second line converges to a single point:
convergent lines

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  • $\begingroup$ For the second one, I would change "rirel frpbaq yvar" to "n frg bs guerr yvarf" [rot13] $\endgroup$ – Jay Apr 15 at 0:58
  • $\begingroup$ @Jay, but several of them have more than three lines, so "every second line" (or perhaps "alternating lines") is a more complete description... Also, because it's less strict, I can find ways to make your rule work on the right hand set. $\endgroup$ – Alconja Apr 15 at 1:16

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