geometry puzzle

[cellio]

You're being too productive; let me help:

World's hardest easy geometry problem, forwarded by a coworker, allegedly solvable with pure geometry (no trigonometry).

Comments

[chaos-wrangler.livejournal.com]

*g* I've printed them out for me & G. Thanks for the "help".

[cellio]

Don't thank me yet. :-)

[metahacker.livejournal.com]

This reminds me of my physics teacher's approach to solving any problem:

Step 1: Draw a diagram.
Step 2: Cross it out and draw a BIGGER diagram.
...

[cellio]

I did that. :-)

[caryabend.livejournal.com]

3) Repeat 1 and 2 as necessary.

4) Try not to be grumpy when your friend studying free market economics makes a killing on paper and writing supplies.

[cellio]

There comes a point when a whiteboard is the right tool. :-) (Ok, what I really want is a stack of transparencies, or the easy electronic equivalent...)

I've derived lots of additional factoids, but they have not yet led to a solution. I'm trying to figure out how to set up the multi-variable system of equations. :-)

[caryabend.livejournal.com]

multi-variable system of equations

I'm pretty sure that's not elementary geometry.

[cellio]

I wasn't sure if that was a legitimate approach (algebra came before geometry in my education), but I didn't go down that path because of the claim of "here is everything you need to know to solve this" farther down on the page (which doesn't mention equation-solving).

[magid.livejournal.com]

multi-variable system of equations

That's where I found myself, too.

[dagonell.livejournal.com]

I did this back in high school. Our math professor used to give out puzzles to solve. First student with a correct solution got a dollar. At the beginning of the semester they were fairly easy
"If 5 cats can catch 5 mice in 5 minutes, then how many cats are needed to catch 100 mice in 100 minutes?" The triangle one was towards the end of the semester, I spent several weeks at it. Hint: Extend line DE down to match AB.
-- Dagonell

[ichur72.livejournal.com]

I think I've solved for X, but I need to see if I can turn it into a proof since my solution involved scissors.

[cellio]

I briefly wondered whether measuring would be legit (proportionally, not with a scale), but concluded that I am not nearly a good-enough draftman to be able to rely on the results. :-)

[ichur72.livejournal.com]

I cheated and checked my solution against Professor Google ... and D'OH! I'm wrong.

[baron-steffan.livejournal.com]

I have an issue with the title. Specifically, define "easy" and "hard". If "easy" means no trig, then aren't we including classic problems like trisecting an angle and squaring a circle? Especially if "hardest" includes "impossible"....%^)

[cellio]

I think the claim is that this is the hardest problem the author knows about for which a solution is known and that does not require trig. That's my read on it, anyway.

[http://users.livejournal.com/merle_/]

Solve all the obvious angles, you'll be left with four (all in the upper sort of area). After applying one simple fact, you're left with four "a+b=something" formulae, four variables, and just solve.

(okay, I admit that I made an intelligent guess at that point rather than solving them, but I got a correct answer... and it should be solvable via algebra. I'm just lazy.)

[giddysinger.livejournal.com]

That doesn't quite work. Everything ultimately reduces down to "the sum of angles AED and BDE equals 130." The solution is going to require more than the "sum of the angles" trick.

(Not saying that either the wife or I have solved it, but still...)

[http://users.livejournal.com/merle_/]

No? Hmm. I got it down to the four angles around the upper line segment that goes through the main triangle, and from there found a solution.

I do admit to looking at the equations, thinking "this feels right", and just trying a number for one of those four angles.

As well as the sum of the angles in a triangle trick, you need the sum of angles coming off of a line trick (ie one line, several lines emerging from a single point on that line, the sum of those angles is 180°).