Use any drawing software like Paint or the like to draw 4 triangles using only 4 straight lines! Also, the borders of your drawing don't count ;)


I think you can draw

any four straight lines.

(As long as no two of them are parallel with each other, and all the six crossing points are distinct from each other.)

This works, because

any three straight lines will always form a triangle, unless either
* some two of the lines don't ever cross (because they are parallel), or
* all three lines cross at the same point.

Since you have 4 lines, you can

choose three of them in 4 separate ways,

so you are guaranteed to always get exactly 4 triangles.

  • 4
    $\begingroup$ Nitpick: this seems to assume an infinite space, which Paint is not. $\endgroup$ – Mark Jan 17 '20 at 13:07
  • 3
    $\begingroup$ @Mark to escape the nitpick on a technicality: the puzzle explicitly says that the borders don't count :-) $\endgroup$ – Bass Jan 17 '20 at 13:44
  • 1
    $\begingroup$ I think that means they don't count as edges of the triangle (somehow I can't tag you sorry) $\endgroup$ – Mark Jan 17 '20 at 13:46
  • 1
    $\begingroup$ @Mark I agree 100%, but I'm going to plead the letter of the law :-) (The poster will automatically get a notification of any comment added to their post, so tagging me here isn't necessary, which is also why it doesn't work.) $\endgroup$ – Bass Jan 17 '20 at 13:53
  • $\begingroup$ @mark you don't need an infinite space (it is never even mentioned in the answer). $\endgroup$ – Mindwin Jan 17 '20 at 14:30

Here's a solution for 4 triangles with 4 straight lines:

Here are the first two triangles:

Here's the third triangle:

Here's the fourth triangle:

In fact,

I suspect that this will work for any triangle formed of three lines with an additional line, so long as the additional line is not parallel to any of the three other lines nor incident to the vertices of the triangle.

  • $\begingroup$ Regarding the final spoiler block: I don't think it's necessary for the fourth line to cross the triangle. Using your diagram as an example: if you draw the lines forming the smallest triangle first, the fourth line doesn't cross it, but everything still works. (I may have also posted an answer to this effect before reading yours all the way to the end.) $\endgroup$ – Bass Jan 16 '20 at 21:45
  • $\begingroup$ @Bass Good point, I'll revise my answer to include that point. $\endgroup$ – Avi Jan 16 '20 at 21:47


My solution to this is as follows:

  • 5
    $\begingroup$ I like this answer best, simple and effective. Live long, and prosper. $\endgroup$ – SwiftPanda Jan 17 '20 at 21:19


The four triangles are:


4 triangles with 4 lines There are multiple ways to obtain 4 triangles from 4 lines. Here is one way you can obtain. The 4 traingles are ABC, ADE, DCF, BEF.

  • $\begingroup$ This appears to be a duplicate of Sarbus' answer $\endgroup$ – Herb Feb 11 '20 at 17:03

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.