What is the most triangles you can make from a capital "H" and 3 straight lines?

Question

So start with an upper case H, and then draw $3$ straight lines. What is the greatest number of closed triangles that you can form? For example:

Note that triangles inside of triangles only count once (e.g. 5 & 6 in the image don't count):

And you aren't allowed to extend the cross line of the H (e.g. 5 in the image doesn't count)

score 25 · Accepted Answer · edited Mar 01 '19 at 14:07

25

Here's a solution for 7 triangles:

edited Mar 01 '19 at 14:07

Ahmed Ashour

answered Mar 01 '19 at 08:41

Bass

1

You can make $8$ from that picture. See if you can figure it out ;) – Mr Pie Mar 01 '19 at 13:48
14

No, you cannot. – Bass Mar 01 '19 at 15:10
1

Decrease the angle between three red lines and rotate them ccw slightly. Now two rightmost red lines in the original form will make another triangle with the right pillar of H. According to OP only extending the cross line is not allowed. – no more sigsegv Mar 01 '19 at 17:13
4

@btw please draw a picture. The two rightmost red lines (the ones that go through the right edge of the picture) already make a triangle with the right pillar of the H, and hopefully you aren't suggesting that three straight lines could somehow make more than one triangle. – Bass Mar 01 '19 at 18:21
3

I was mistaken! After lots of analysis from drawing at home and all, methinks $7$ triangles is, in actual fact, the maximum amount that can be made from $3$ straight lines and with the OP's rules. My apologies! But, to your answer, my compliments! :D – Mr Pie Mar 02 '19 at 06:40

score 6 · Answer 2 · answered Mar 01 '19 at 01:47

6

Here's one with six triangles (7 if you count triangles outside of triangles, which you don't):

answered Mar 01 '19 at 01:47

Brandon_J

1

I suspect that this is the highest that can be gotten, but I'm not sure. – Brandon_J Mar 01 '19 at 01:52
My friend alleges that he can get 7, but won't show me how. Considering writing a python script to help prove that 6 is the max. Also I feel like there may be a mathematical proof of this with analytical geometry – Curtis Mar 01 '19 at 05:07
1

If you just moved all of your blue lines up or down a bit you’d get 7 won’t you. – tyobrien Mar 01 '19 at 15:38
3

@tyobrien you'd get one more triangle in the middle, but the two triangles right next to the new one would become quadrangles, right? – Bass Mar 01 '19 at 15:55
Oh yes that would be correct – tyobrien Mar 01 '19 at 15:56
Oh yeah @bass lol – Brandon_J Mar 01 '19 at 18:40

score 3 · Answer 3 · edited Mar 01 '19 at 14:01

3

Does this count as 8 triangles?

edited Mar 01 '19 at 14:01

Ahmed Ashour

answered Mar 01 '19 at 09:28

2

The question says "Note that triangles inside of triangles only count once", which (I think) is a more complicated way of saying "the triangles are not allowed to overlap". – Bass Mar 01 '19 at 09:32
@Bass Precisely! – Curtis Mar 01 '19 at 14:12
@Bass it is possible to create two triangles that overlap, but neither is inside the other, so they're not just different ways of saying the same thing. – Monty Harder Mar 01 '19 at 15:31

score 0 · Answer 4 · answered Mar 01 '19 at 13:39

0

Please have a look at this pic using 3 red lines on letter H. I count 10 triangles

answered Mar 01 '19 at 13:39

bi_noob

10

Overlapping triangles are not counted, so there are only 5 in your arrangement. – Jaap Scherphuis Mar 01 '19 at 13:41
Yeah, I agree with @JaapScherphuis – Brandon_J Mar 01 '19 at 18:41
@JaapScherphuis Event with overlapping I count 6. How are there 10 here? – Hazel へいぜる Mar 01 '19 at 22:33
@PerpetualJ I count 10 with overlapping rot13(gbc bs gb u gb zvqqyr yvar gvzrf gjb naq gbc bs u gb obggbz erq yvar gvzrf gjb. ) not sure if that helps – Yout Ried Mar 01 '19 at 23:50

4 Answers4