A sign manufacturer makes yield signs by cutting N identical-sized equilateral triangles from a square piece of aluminum; N is at most 25. What is the most efficient use of aluminum: what is the optimal value of N and what percent of the aluminum is used in yield signs?

Question

unklerhaukus · Answer

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optimal value for N is 16
because you get 100% efficiency

anonymous · Answer

those aren't yield signs! (equilateral triangles)

unklerhaukus · Answer

i thought it was isosceles, 
sorry, my answer is wrong

unklerhaukus · Answer

http://www2.stetson.edu/~efriedma/triinsqu/

anonymous · Answer

awesome! 

n = 24 gives an example with better than 86.4% of the metal being used in yield signs. 

The n=4 example shows almost 70%; the case n=7 is crazy beautiful using equilateral triangles of side length exactly half the square. 

Since those pictures are repeated in MathWorld and CRC as "best known," I think I'll put this problem into the category "Unlikely to be solved with proof during my lifetime."