![]() And I’ll be waiting.The nine dot problem is a classic lateral thinking exercise that gained widespread popularity in the 1970's and 80's. I haven't quite thought of how to quantify each suggestion (and applying the latter after the former would increase the count still), so I don't have an easy number for you to use in an updated important update (if you found my ideas worthwhile to update). Of course, exceptions are made for isoscolese and equilateral triangles (the latter would only have 3 distinct triangle definitions). If we were to apply that to the triangle (and relax the right-angle requirement, it might mean that BAC is different than CAB. If we then take a particular case, right-angle triangles, we can derive sine, cosine, and tangent functions (SOH, CAH, TOA). I suggest that t-two, being described by BAC, is different. Given a triangle T, with vertices A, B, and C, t-one might indeed be described by ABC, with B being the central angle. Would not the areas of the mini-triangle and the area of the rhombus adjacent to it, combined, make for another triangle? Another idea for consideration: Triangles have 3 angles (who would have guessed?) however, I would postulate that how you describe a triangle, by way of said angles, would generate different triangles. Take, for example, the bottom-left mini-triangle in the "Important Update" addendum. Reader James Goodrich took it another step further, suggesting we open our minds to consider what a triangle could be: Well, according to your reader, who pointed out 17 additional triangles (using the "Andrew didn't specify what lines can comprise the 3 edges of a triangle" clause), failed to clearly find quite a lot more. The good news is that this confirms that life clearly DOES have meaning, as evidenced by the exact number: 42. The bad news is that we missed some triangles. This bring the total number of triangles up to 42. Poingly While some of these MAY be somewhat debatable (ie, where EXACTLY do the light blue lines intersect the dark ones and do they technically form a triangle or a quadrilateral), I have counted SEVEN ADDITIONAL triangles that may be made in this way. One reader, Ralph Linsangan, totally owned me by sending this image, in which he marks every additional triangle found under the technicality, flagging 17 additional triangles for a total of 35. ![]() I never specified to only use those dark blue lines, and thus, I am wrong. I unfortunately drew this triangle on lined paper, and lots of smart people have correctly pointed out that, well, actually, if you count the light blue parallel lines in the image in addition to the dark blue lines written in marker, there are actually more than 18 total triangles here-considerably more. I could have made this much easier on readers-and, crucially, much easier on my inbox-had I just sketched the triangle on plain, white computer paper. □ IMPORTANT UPDATE 1/30/20□: Since publishing this story, many, many readers have reached out to let me know that while 18 is indeed an acceptable answer to this problem, it isn’t the only one, due to some unintentional oversight on my part. But it’s only a matter of time before they discover it-and argue some more. I haven’t shared this new triangle problem with my coworkers yet. “If you took the same seven lines and shook them up a bit, probabilistically they’d most likely land like problem and you’d have more triangles and a similar cute answer.” (For the record: 35.) ![]() In the picture I sent her, some lines are parallel, so they can’t be part of the same triangle. “In that case, every pair of lines intersects and there are no triple-or-more intersections, so any choice of three always gives a triangle,” says Mangahas. ![]() 10 of the Hardest Math Problems Ever Solved.The Amazing Math Inside the Rubik’s Cube.How to Solve the Infuriating Viral Math Problem. ![]()
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