I recently received a tough puzzle as a gift from my brother. The name of the puzzle is “Orchard”, and so far, indeed, it seems quite tough! The first step in solving it is to solve this puzzle :

- Get a blank sheet of paper,
- Draw 10 dots on the page
- Get a ruler and rule five straight lines, but
**make sure each line passes through four dots.**

Of course, to solve this puzzle means you’ll have to get the dots in the right places first!

You could extend this puzzle, for example –

- draw 4 lines, making sure each line passes through 5 dots, using as few dots as possible in total
- draw 7 lines, making sure each line passes through three dots, using as few dots as possible in total

Of course, there’s no limit to the variations on this problem. You could also turn it around –

- Draw 20 dots on the page. How many straight lines can you draw with at least 4 dots each? Can you get more straight lines if you draw the dots in different places?
- Draw 31 dots. How many straight lines can you draw with at least 5 dots each?