The World's Hardest Easy Geometry Problem

Discussion in 'General discussions' started by smhbbag, Nov 13, 2008.

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  1. smhbbag

    smhbbag Puritan Board Senior

    World's Hardest Easy Geometry Problem

    The directions are there, but I'll post them:

    The figure is at the link.

    Have fun. :think:

    At first glance, my first thought was "that's trivial." But it's not. Many times I thought I had quick solutions, and I did not. Yall enjoy, and without wasting much more of my own time, I'm simply going to trust the mathematicians who have said elsewhere that it is genuinely hard.

    I feel like a sham of a math tutor, now.
     
  2. smhbbag

    smhbbag Puritan Board Senior

    bump for the evening crowd.

    I looked up the solution online and it's.....ridiculous. I could've spent a few more days on it and never got it.
     
  3. OPC'n

    OPC'n Puritan Board Doctor

    That's not what I call fun! You need to get out more! :lol:
     
  4. BJClark

    BJClark Puritan Board Doctor

    I am NOT a math person, so I passed it along to my daughter whom I know it will bug the day lights out of until she figures it out..she's trying to work it out now..
     
  5. BJClark

    BJClark Puritan Board Doctor

    She says it's X degrees..

    I can delete the answer if others want to figure it out on their own...it took her less than 10 minutes..
     
    Last edited: Nov 13, 2008
  6. Calvinist Cowboy

    Calvinist Cowboy Puritan Board Junior

    I guess I must be a math geek then. This was challenging!
     
  7. BJClark

    BJClark Puritan Board Doctor

    Calvinist Cowboy;


    she didn't find it very challenging at all, she followed the first hint-- pulled out her protractor, had it solved in minutes..

    Had I been trying to solve it, I'd be here for days...getting frustrated..not worth that to me..
     
  8. smhbbag

    smhbbag Puritan Board Senior

    Protractors are cheating :lol:
     
  9. Seb

    Seb Puritan Board Junior

    I got the answer...but I had to use AutoCad to get it.

    This one's very hard.
     
  10. BJClark

    BJClark Puritan Board Doctor

    smhbbag;


    Using any of the hints would be cheating..but she looked at the hint and took advantage..
     
  11. VictorBravo

    VictorBravo Administrator Staff Member

    Thanks for posting this. It was remarkably challenging (if you agree to use only elementary geometry).

    But the solution is easy, once it jumps out at you. It took me all evening.
     
  12. Zenas

    Zenas Snow Miser

    I have a few questions before I begin to answer the question:

    1. What is "x"?

    2. What is an angle?

    3. What is a proof?

    4. What is geometry?

    -Thanks.
     
  13. smhbbag

    smhbbag Puritan Board Senior

    What was your solution? No offense, but I'm willing to bet you're wrong. If not on the solution, then probably on the proof :)

    The full proof and answer is here

    相忘于江湖
     
    Last edited: Nov 15, 2008
  14. VictorBravo

    VictorBravo Administrator Staff Member

    Heh. I don't have a way right now to post my scatchings that are on a scrap of paper, but my solution was similar to his. I followed a slightly different path, but applied the same concepts. Certainly identifying the various isosceles triangles and bisecting angles with perpendiculars was key.

    Instead of an equilateral triangle in the middle, I developed a mirror image of the triangle containing the angle x that I called EDG. G is a point on the perpendicular bisecting angle CDB. And then I drew a line from point D to what I called point H that was parallel to line AB.

    From that, it was a matter of bisecting angle ACB and then staring at all the angles to realize the realtionships.
     
  15. smhbbag

    smhbbag Puritan Board Senior

    Well, then I humbly retract my skepticism, and award you the amount of 1 Thanks for your effort :) I was unable to get it after a little less than an hour, and looked up the solution. Bravo.
     
  16. Zenas

    Zenas Snow Miser

    Victor Bravo.
     
  17. smhbbag

    smhbbag Puritan Board Senior

    :lol:

    Nice.
     
  18. VictorBravo

    VictorBravo Administrator Staff Member


    Well, it took me a lot longer than an hour. I started thinking about it last night and probably drew triangles and lines in my head for maybe an hour last night before I fell asleep. Then I fiddled with it this evening for about 3 hours. It is a doozy.
     
  19. VictorBravo

    VictorBravo Administrator Staff Member

    I don't know why, but I love these kinds of problems.

    For what it's worth, I finally got my proof cleaned up and into a web suitable form. It is quite similar to the answer already posted, but I think the graphics help explain it a bit.

    [​IMG]

    [​IMG]

    [​IMG]

    So GF equals DF which equals EF. Triangle DEF is isosceles. This means that angle DEF equals angle EDF.

    Angle DFE equals 80 because DF is parallel to AB. Angle DEF is found by subtracting 80 from 180 and dividing by 2, which equals 50.

    Simple addition tells us that AEB is 30 degrees. Angle x is therefore 50 - 30 = 20
     
  20. CIT

    CIT Puritan Board Post-Graduate

    I thought I was going to get this problem eventually, but I was wrong. I guess I don't remember my geometry as well as I use to.
     
  21. smhbbag

    smhbbag Puritan Board Senior

    I think it's a lot more about creativity than knowing the rules. So, it's not really a knock on our memories, just our problem-solving skills :lol:
     
  22. CIT

    CIT Puritan Board Post-Graduate

    Oh if that is the case.......:rolleyes:



    :lol::lol::lol:
     
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