Did you solve it? The joy of grids

On the grid: a scene from 1982 film Tron. Photograph: Allstar/Cinetext/DISNEY

On my puzzle blog earlier today I set you the following three problems about this grid:

1. A polygon is a shape where each side is made from a straight line. Draw a polygon in the grid with 16 sides. (Note: Each side of the polygon must join two dots. Lines cannot overlap. The shape must have no gaps in its outline, and each dot can be visited at most once.)
   

Solution. Here’s one shape that works.

2. Find the 20 squares that can be made by joining four dots.

Solution: Thinking orthogonally, we get 9 1x1 squares, 4 2x2 squares, and 1 3x3.

Thinking diagonally, we get 4 at a 45 degree angle, and 2 at the lesser angle. Summing them up makes 20 in total.

3. Find a way to connect all 16 points with an acute angle at every point.

Solution:

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

Thanks again to Daniel Finkel for today’s puzzles.