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This is "fifteen triangles":

▲ ▼ ▲ ▲ ▼ ▼ ▲ ▲ ▲ ▼ ▼ ▲ ▲ ▲ ▼ ?

Each triangle points up or down. What the "?" figure should be and why?

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    $\begingroup$ Probably a triangle, because the rest are triangles. $\endgroup$ – Vaelus Mar 10 '18 at 22:05
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    $\begingroup$ the next figure is "7", and there's no way to prove otherwise. $\endgroup$ – Peter Mar 11 '18 at 9:19
  • $\begingroup$ Given the "lateral thinking" tag, surely the next figure is ▶ . $\endgroup$ – wchargin Mar 11 '18 at 19:43
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It should be

Pointing upwards

Because

Every letter in "fifteen triangles" is represented: consonants=up, vowels=down. Since the last letter is a consonant ("s"), it should point up.

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    $\begingroup$ Reminds me of xkcd.com/169 $\endgroup$ – jpmc26 Mar 11 '18 at 19:12
  • $\begingroup$ @jpmc26 What Th--AaAAaaAAAaaAAAaA! $\endgroup$ – R.M Mar 12 '18 at 0:37
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On account of the lateral thinking tag, I'd say the sixteenth figure is...

The question mark at the end.
It's never stated that the sixteenth figure is a triangle in the title or body.

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  • $\begingroup$ edited the question a bit $\endgroup$ – enkryptor Mar 10 '18 at 13:50
2
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Given the tag "lateral" thinking, I'm not sure the current pattern is enough to dictate a single potential pattern and so there could be a fair number of possible ways the sequence could go.

However I'll guess the next triangle is:

Because:

The pattern is reversed at the point of the second set of 2Xdown (▼ ▼)

The pattern given is:

▲  ▼  ▲ ▲  ▼ ▼  ▲ ▲ ▲  ▼ ▼  ▲ ▲ ▲  ▼
           |ii|  |i|   |A|   |B|

A = The reverse is activated
B = The next set of characters from being reversed at "A", which is denoted as "i"
ii = The next set of characters in the (now) reversed sequence

Your completed sequence would look like:

▲ ▼ ▲ ▲ ▼ ▼ ▲ ▲ ▲ ▼ ▼ ▲ ▲ ▲ ▼ ▼

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0
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The sixteenth triangle is

Because:

The pattern at the end seems to be 2 ▼ and 3 ▲

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  • 1
    $\begingroup$ what about the beginning of the sequence? $\endgroup$ – enkryptor Mar 10 '18 at 14:26
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    $\begingroup$ it's a red herring $\endgroup$ – Peregrine Lennert Mar 10 '18 at 14:33
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    $\begingroup$ no, it is not :) $\endgroup$ – enkryptor Mar 10 '18 at 16:40
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The next triangle is:

Because

The overall sequence is {1,2,3,3} UP triangles, with {1,2,2,1} DOWN triangles in between. The next group of triangles will be pointing up, since it's their turn. There will be 2 of them in this group because their pattern sequence (reflecting the down triangle's pattern) is {1,2,3,3,2,1}.

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