An equilatteral triangle is a triangle in which all three sides have the same length. How can one arrange six equal-length match sticks so that the result contains four equilatteral triangles?

I actually like the 3d solution better, and I think this one's kind of dumb, but at least you don't get a diamond shape in the middle...

make an equlateral triangle with the bottommost line (A) being horizontal. The other two lines we'll name B and C. Each of the three lines should extend well past where it crosses the other two. Make a fourth line parallel to the bottom horizontal but crossing B and C at their endpoints ABOVE the triangle, Now rotate the setup so that B is the bottom horizontal, make a line parallel to it and treat it in the same way we did with A. Do that for C and its copy as well. Now we've got six lines and four equilateral triangles all with lines extending past their vertices. Oh happy day!

Posted by Carey on 2002-05-28 10:11:42