Re: The hardest Euler problem

Albert van der Horst wrote:
> I have sorted the Euler problems from hardest to easiest,
> and indeed the most interesting ones come up front.

As far as I can tell, the "difficulty" metric is the number of correct 
solutions submitted with no factoring for the amount of time posted, and 
as such, can be a bit misleading.

> 
> This one gets me particularly stunned.
> 
> Find all quadrilaterals with angles (including those with diagonals).
> that can be measured in whole degrees.

Slight restatement: find all convex quadrilaterals such that the angles 
between the sides and the interior diagonals can be measured in whole 
degrees.

 > I cannot come up with something better than this
 > - guess all angles except one.
 > - calculate the last one using goniometric functions.

If the angles between two adjacent sides and the diagonal are both whole 
number of degress, then the angle between the sides will be as well.

A better approach might be to start by findibg all of the integer anged 
triangles, and then enumerating the quadrilaterals that can be built 
from it.

I am working on problem 176 first, because it enumerates triangles, and 
if I understand it, I suspect that 177 might be easier for me.

> Groetjes Albert

-- Charles
(cac, 52%, 99/191)