Join the Dots: The Sharpest Path Wins

Impressed by one other connect-the-dots grid puzzles, I’ve developed a variant with a novel set of motion restrictions. It’s related in spirit, however with a twist: you’ll be able to solely transfer instantly from dot to dot, with no free-form motion allowed.

The target is to attract a single, steady line that connects as many dots as doable on a 5×5 grid with out crossing itself.

The Grid

The puzzle is performed on a 5×5 grid of dots:

•   •   •   •   •

•   •   •   •   •

•   •   •   •   •

•   •   •   •   •

•   •   •   •   •

The Guidelines

1. Steady Line: The road have to be a single, steady path.
2. No Repeated Dots: The road can’t go to the identical dot greater than as soon as.
3. No Crossing Over: The road can’t cross over a beforehand drawn phase. (e.g., a diagonal transfer can’t "soar" over an current horizontal or vertical line phase).

4. Particular Motion Rule (The "Reverse Flip" Rule): That is the core of the puzzle. After your first transfer, you at all times have two selections: go straight, or make a particular "reverse" flip.

   a) Go Straight: You’ll be able to at all times repeat your final transfer. For those who simply went Proper, you’ll be able to go Proper once more.

   b) Make an "Reverse Flip": To show, you will need to transfer in a means that partly reverses your final course.

   • In case your final transfer was DIAGONAL…

     Instance: You moved Down-and-Proper. A standard flip is perhaps Down or Proper. However for an "reverse flip," you will need to use the reverse straight instructions. Your solely doable turns are straight Up or straight Left.

   • In case your final transfer was STRAIGHT…

     Instance: You moved straight to the Proper. To make an "reverse flip," your subsequent diagonal transfer should embody the reverse horizontal course (Left). Your solely doable turns are Up-and-Left or Down-and-Left.

   The Large Concept: Turns are at all times "backwards-looking." A diagonal transfer turns into its reverse straight elements, and a straight transfer turns into diagonals that return on themselves.

Predominant Problem:

• What’s the most variety of dots you’ll be able to join on a 5×5 grid following these motion guidelines?

Bonus Problem:

• What’s the most variety of dots you’ll be able to join on a 7×7 grid following these motion guidelines?

Superior Problem:

• What’s the most variety of dots you’ll be able to join on a n×n grid following these motion guidelines?

Interactive Model

To make exploring the puzzle guidelines and mechanics simpler, I’ve created a totally playable model. You’ll be able to simply share your resolution by taking screenshot from it.