A - B - C / \ / \ / \ D - E - F - G / \ / \ / \ / \ H - I - J - K - L \ / \ / \ / \ / M - N - O - P \ / \ / \ / Q - R - S
Place the numbers 1-19 in the hexagon, such that each of the twelve triangles
of six numbers have the same sum. These include triangles such as ABCEFJ and
BEFIJK. What are the lowest and highest
possible common sums?
Extension: Find a solution which also has these sets equal to the common sum: the six corners (ACHLQS), the six sides (BDGMPR), and the six central values (EFIKNO).