# There are fifteen triangles, what is the sixteenth?

This is "fifteen triangles":

▲ ▼ ▲ ▲ ▼ ▼ ▲ ▲ ▲ ▼ ▼ ▲ ▲ ▲ ▼ ?

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

• Probably a triangle, because the rest are triangles. Mar 10, 2018 at 22:05
• the next figure is "7", and there's no way to prove otherwise. Mar 11, 2018 at 9:19
• Given the "lateral thinking" tag, surely the next figure is ▶ . Mar 11, 2018 at 19:43

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.

• Reminds me of xkcd.com/169 Mar 11, 2018 at 19:12

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.

• edited the question a bit Mar 10, 2018 at 13:50

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:

▲ ▼ ▲ ▲ ▼ ▼ ▲ ▲ ▲ ▼ ▼ ▲ ▲ ▲ ▼ ▼

The sixteenth triangle is

Because:

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

• what about the beginning of the sequence? Mar 10, 2018 at 14:26
• it's a red herring Mar 10, 2018 at 14:33
• no, it is not :) Mar 10, 2018 at 16:40

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}.