Rather than trying to cross every line segment just once, label the vertices of this network with values of 1 through 12 such that the sum of the intersections which lie on the perimeter of the internal quadrilaterals is the same.

With a multitude of solutions abound these following impositions are to be applied separately/individually as well:
1. L4=L5 and 3*L1 = 4*L3
2. L4=L5 and 2*L1 = 3*L3
3. L4=L5 and L3<10
where L1=A+B+C+DAA L2=E+F+G+H+IAA
AAAAL3=J+K+LAAAAAAL4=A+E+JAA
AAAAL5=D+I+L.

Each impost has 2 solutions which are not reflections. How many can you find?

brianjn, what is meant here by vertices, and how do the uppercase letters A to L relate? The question arises as some of the letters do not appear to be labelling vertices and some of the vertices are not labelled. Are the letters to represent only positive integers? From imposition 3, it is implied that they might even represent multi-digit integers but that is not definitive either.

Posted by Dej Mar on 2012-04-11 01:02:49