Dot-to-dot puzzles that hit the spot

Hi guzzlers,

Today, three challenges using this grid of 16 dots:

1. A polygon is a shape where each side is made from a straight line. The H polygon below has 12 sides and the K has 13 sides. *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.)

2. Below is a single square made by joining four dots in the grid. *Find the other 19 squares that can be made by joining four dots.*

3. Below is a way of connecting 14 of the points with lines, such that the angle at every point is acute, i.e. less than 90 degrees. *Find a way to connect all 16 points with an acute angle at every point. *

Today’s puzzles are set by Daniel Finkel, an inspirational maths educator from Seattle. “Grids are one of the most familiar objects we know,” he says. “And yet it sometimes feels like we know nothing about them at all. There’s so much mystery in such a simple arrangement!”

The solutions to today’s puzzles, he adds, are all hiding in plain sight. “There’s something I like about that, because once you see it, you keep noticing it. I like a puzzle that stays with you, and changes the way you view things.”

I like these puzzles too because to solve them you are essentially doodling, and who doesn’t like to doodle? They also lead quite quickly to deep ideas in different mathematical fields. You might want to ponder, for example, the above questions for larger grids, and see what patterns come up…

If you do want to ponder, please ponder below the line!

I’ll be back with the answers at 5pm GMT.

*Thanks to Daniel Finkel for today’s puzzles. His website, which contains free maths education resour**ces, is mathforlove.com. He has also produced two award-winning maths games for kids: Prime Climb and Tiny Polka Dot. Check them out! Today’s puzzles are adapted from a column he writes for The Hindu.*

*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.*

*I’m the author of several books of popular maths, including the puzzle books Can You Solve My Problems? and Puzzle Ninja.*