World’s Hardest Easy Geometry Problem
I’ve been puzzling over this for the last two hours.
At first I thought it was trivial.
Since then I’ve constructed many parallel lines, summed many sets of angles to 180 degrees, noted opposite angles, set up simultaneous equations…and still haven’t solved it.
If you happen to figure it out, please don’t tell me the solution.
December 3rd, 2007 at 12:46 pm
Travis–
Using “M” to denote the point where lines BD and AE cross, I think what you need to do is prove that triangles CDE and BEM are congruent. Unfortunately, I can’t remember how to do that, since it’s been too long since I’ve done geometry. . .
December 3rd, 2007 at 3:40 pm
I’m reminded of the fact that the “elementary” proof of the Prime Number Theorem is far more complicated than the proof using complex analysis.
December 3rd, 2007 at 3:55 pm
I might have gotten the wrong answer, but still, it only took me five minutes and strikes me as an easy problem. Of course, my thinking process is based entirely on angles. That’s why flat things confuse and aggravate me. SCOTT SMASH PLANE!
December 3rd, 2007 at 5:17 pm
[quote comment="106806"]I might have gotten the wrong answer, but still, it only took me five minutes and strikes me as an easy problem. Of course, my thinking process is based entirely on angles. That’s why flat things confuse and aggravate me. SCOTT SMASH PLANE![/quote]
I got it once, in five minutes, but I was wrong. Then I got it again 30 minutes later, a different way…and I was wrong again.
Maybe you did get it in five minutes.
If/when I solve it myself I’ll compare answers with you.
December 3rd, 2007 at 5:54 pm
[quote comment="106780"]Using “M” to denote the point where lines BD and AE cross, I think what you need to do is prove that triangles CDE and BEM are congruent. Unfortunately, I can’t remember how to do that, since it’s been too long since I’ve done geometry. . .[/quote]
Triangles CDE and BEM are not congruent. You can verify this with the “ruler method” on the large to-scale diagram on the puzzle site. (This was the solution I considered at first, too.)
Damn — this is hard! I spent about 5 minutes on it, then realized I had work to do. I’ll come back to it later if I get my work done (so, probably never). Where has my sense of intellectual curiosity gone?
December 3rd, 2007 at 5:56 pm
[quote comment="106818"]Where has my sense of intellectual curiosity gone?[/quote]
Oh, I’ll add that the printed version of the puzzle makes a delightful crackling sound when I throw it into my fireplace, though. The angles don’t seem to matter there.
December 3rd, 2007 at 8:30 pm
Solving it is easy, its proving it using basic geometry that is hard. I solved it quick but 6 hours later I still can’t prove it. The answer is 20 degrees, but you can get that using a protractor…
Has anyone solved it without using a circle? I don’t think a circle is fair…
December 4th, 2007 at 1:04 am
You suck Travis. I have about 12 copies of this stupid drawing with numerous lines all over them trying to find the right set of triangles and parallel lines. Still no solution, but on the bright side I may be able to sell the collection of my various attempts to an art gallery doing a Mondrian retrospective
December 4th, 2007 at 11:50 am
Bashed my brain against it hopelessly last night, then it came out fairly easily this morning. Send me email if you want a hint.
I’ve made absolutely no progress with the “second hardest …”.
February 12th, 2008 at 6:01 pm
Hey guys. I am twelve. I figured out the answer and written a full proof. There really is not much too it. Just take some time to actually think about the problem. o and by the way, X = 20 degrees, just in case you haven’t gotten it yet. I did NOT use a circle. I only prolonged some lines. There is a hint right there
February 12th, 2008 at 6:47 pm
Damn! Give that kid a job!
October 13th, 2008 at 10:32 pm
x=40
record 5 min.
it’s right
June 27th, 2009 at 9:41 am
I didn’t sleep for 27 hours and I got to 30 degrees!