Tuesday/ point and line puzzles

I scan through the Wall Street Journal almost every day, at the public library here in my neighborhood. The weekend edition has puzzles in, and the two puzzles below are from this last weekend.  (This is the link to the WSJ puzzle blog).

I think I know the solution to the ‘Maximizing Links’ problem .. but the Seven Points problem has me stumped .. but I’m working on it!

Update Fri 4/6: Well, the solutions have been published. I got the first one right: 9 links can be drawn. Trying to solve the ‘Seven Points’ problem was a humbling experience, and I got close, but no cigar.  I knew the solution had to involve equilateral several connected triangles, but I should have applied more rigor, and maybe used a compass to arrive at the solution (as shown in the figure with the circles, from Math Stack Exchange).  So depending on the way one looks at it, the solution is a regular pentagon, with two points carefully added to it, equidistant to three other points on the pentagon .. OR two diamonds pinned at a shared vertice (bottom left on the first diagram), and the other vertices a unit length apart.

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