# Multiple Line Lengths around 8 triangles

The image below contains 8 triangles each having side length 6.

Inside each triangles are three numbers indicating lengths of 3 lines that are wrapped around the triangle without gaps.

Numbers range from 2 to 10 with not all numbers appearing inside each triangle the same number of times.

This is the rule. If the line of length 10 is 6 long then turns then it must be the same in every triangle it appears in.

You'll notice that in the image below that the line of length 3 is completely straight in the bottom triangles where it appears but in the top triangle the space for it to fit needs a bend. Also notice that the line of length 6 is also broken in this example solution. In three triangles the 6 is a straight line, but in the top triangle its forced to bend once Question 1 Is it possible to fit all the lines around all the triangles where the lines all stay a constant shape within each triangle they appear?

Question 2 Is it possible to to achieve the above solution with the 8, 9 and 10 lines only bending once.

Note.
Possible lines
2 - straight 2 or bent (1,1)
3 - straight 3 or bent (1,2)
4 - straight 4 or bent (1,3) (2,2)
5 - straight 5 or bent (1,4) (2,3)
6 - straight 6 or bent (1,5) (2,4) (3,3)
7 - 1 bend (1,6) (2,5) (3,4)
8 - 1 bend (2,6) (3,5) (4,4) 2 bends (1,6,1)
9 - 1 bend (3,6) (4,5) 2 bends (1,6,2)
10 - 1 bend (4,6) (5,5) 2 bends (1,6,3) (2,6,2)

Thats all possible line lengths with bends.

• Are reflections considered equivalent? I.e. All your 10's in the example are split 6,4 reading clockwise. Would a 10 that was split 4,6 (so the mirror image shape) be allowed?
– fljx
Feb 21 at 8:34
• Yes if the 10 line is 6,4 then it must be 6,4 in all other triangles. But it can be reflected and rotated as long as its still a 6,4 line
– Maff
Feb 21 at 12:03
• Do you know the answers to your questions? rot13(Hayrff V unir zvffrq fbzrguvat, vg vf abg cbffvoyr.) Feb 21 at 21:05
• Not at all. I wonder if its possible
– Maff
Feb 21 at 21:51