World's hardest easy problem

  1. jcsd
  2. I haven't the solution, I get the equation x + y = 130, where x and y are angles. If [itex] x, y \in Z^+[/itex]
    This is a diophantine equation. We know: x, y > 0. y > x. And y is greater than 90 degrees.
    the most probable angles:
    [itex] x=20^o\,\, ,y=110^o[/itex]
    or
    [itex] x=30^o\,\, ,y=100^o[/itex]
     
    Last edited: Sep 3, 2013
  3. reenmachine

    reenmachine 521
    Gold Member

    I tried a couple of things but didn't solve it yet , but there's probably a way to build your way up to the x angle using the tricks in my sketch (just don't have the patience to construct the triangles properly and doing it now):
     

    Attached Files:

    Last edited: Sep 3, 2013
  4. Integral

    Integral 7,341
    Staff Emeritus
    Science Advisor
    Gold Member

    Simple geometry is all that is required.

    Why can't you do this for yourself? Don't give up so easy.
     
  5. wazz it,
    i tried it hard thats why asking askin solution,
    well i need an approach
    i asked it to one of my faculty at coaching and he straightaway said it's wrong so i needed to check
     
  6. whatss y in equation
    x+y= 130

    reenmachine i agree myself i even not have patience and doing it (doing angle sum property question) , thanks for tip of parallel lines but what benefit it does
     
  7. reenmachine

    reenmachine 521
    Gold Member

    I don't know since I didn't solve it.It was just a suggestion of strategy to attack the problem , maybe it's a dead end , but the parallel lines will at least allow you to chase more angles , whether or not they end up being useful to find angle x.

    If you don't have the patience to try it , I suggest you do not ask others to do it for you as it's not recommended on the forum to ask for answers without showing that you tried hard before hand.I'm not a moderator , just friendly advice.Also , saying that you tried hard is not showing that you tried hard.
     
    Last edited: Sep 4, 2013
  8. till here i ve done (in attchment)
    one of image is inverted
    so i did the mirror image from webcam toy
     

    Attached Files:

  9. reenmachine

    reenmachine 521
    Gold Member

    You should draw the triangles/angles to scale if you want to try that strategy.

    It should look like the picture below
     

    Attached Files:

    Last edited: Sep 4, 2013
  10. however i got that but i also meant that diophtine (whatever is name) equation

    well where is it taught
     
  11. does that help, because doing any of olympiads we were never told to draw to scale and i was always of kind to do geometry of this kind mentally so it's quite difficult for me
    though i think i'll print that page
     
  12. Uff! After long work with a correct precise figure i bored and saw solution on one of other web pages

    is it bad of me not getting it (i'm 15 yrs and preparing rmo and iit)
     
  13. reenmachine

    reenmachine 521
    Gold Member

    I don't know , you should listen to your teachers before you listen to me that's for sure :tongue2:

    You should also listen to mentors here as they are qualified to help you.
     
    Last edited: Sep 4, 2013
    1 person likes this.
  14. reenmachine

    reenmachine 521
    Gold Member

    Might try to prove both of these triangles (or another pair of triangles) are similar to prove x = 20 :
     

    Attached Files:

    Last edited: Sep 4, 2013
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