# 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. – Vaelus Mar 10 '18 at 22:05
• the next figure is "7", and there's no way to prove otherwise. – Peter Mar 11 '18 at 9:19
• Given the "lateral thinking" tag, surely the next figure is ▶ . – wchargin Mar 11 '18 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.

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 – enkryptor Mar 10 '18 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? – enkryptor Mar 10 '18 at 14:26
• it's a red herring – Peregrine Lennert Mar 10 '18 at 14:33
• no, it is not :) – enkryptor Mar 10 '18 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}.