# The triangle-sequence riddle

this is my number sequence:

/ - / - 1 - 2 - 7 - 6 - ?

This riddle has somtething to do with equilateral triangles
Good luck and have fun :)

this is my first number-sequence level

• Are these dashes intentional? Are they part of the puzzle? If not, what do they mean? – Wais Kamal Nov 7 '18 at 15:19
• @WaisKamal They are part of the puzzle. They mean as you might think idk/not there/undefined – user52327 Nov 7 '18 at 15:24
• Another question, is this the start of the sequence or just a part of it? – Wais Kamal Nov 7 '18 at 15:26
• @WaisKamal This is the start, mark a '1' over the first slash if you like – user52327 Nov 7 '18 at 15:26
• @WaisKamal wait ... did you mean with dash the hyphens or the slashes? Because i meant the slashes with idk/not there/undefined, the hyphons are just to seperate – user52327 Nov 7 '18 at 16:30

impossible? (or '/' as per the question)

Assuming

The constructed shapes must only have acute interior angles, it is impossible to make a heptagon with equilateral triangles

An explanation is given by this picture

Original Guess

8

Each number is in the sequence correlates to:

The number of equilateral triangles required to build a shape which has the corresponding number of sides:

1 and 2-sided shapes with straight edges don't exist in 2D, hence the lack of values.
A 3-sided shape takes 1 triangle (it's already a triangle :P )
A 4-sided shape takes 2 triangles (a diamond)
A 5-sided shape takes 7 triangles (an irregular pentagon)
A 6-sided shape takes 6 triangles (a regular hexagon)
A 7-sided shape can be made with 8 triangles, the next number in the sequence

Like so:

• You're close but not right. – user52327 Nov 9 '18 at 8:49
• Any closer? I'm outta answers if this one is wrong – Dmihawk Nov 9 '18 at 8:54
• I can tell you: the forms you drawed, except the last one are all correct – user52327 Nov 9 '18 at 8:56
• So my new assumption is wrong? – Dmihawk Nov 9 '18 at 8:57
• the last shape is incorrect. your logic has a fault – user52327 Nov 9 '18 at 8:59