Zip Logic Game as a TSP via Constraint Programming

Understanding the Zip Logic Game and Its Real-World Applications

Introduction

What is the Linkedin Zip Logic Game?

Zip is a simple yet challenging puzzle game where the goal is to connect numbered dots in the correct order while filling every cell in the grid. The key challenge lies in planning an efficient path that follows the sequence of numbers without leaving any space uncovered. Some levels include barriers that force you to think ahead and find alternative routes.

This game tests your logical thinking, problem-solving, and spatial awareness as you figure out the best way to navigate the grid. It might seem like just a fun brain teaser, but the logic behind it is deeply connected to real-world optimization problems.

How Zip Relates to Real-World Problems

The way you solve Zip puzzles is very similar to problems faced in logistics, transportation, and automation. In particular, it closely resembles the Travelling Salesman Problem (TSP), which focuses on finding the most efficient way to visit multiple locations while minimizing travel distance and cost.

Here are some real-world applications where similar logic is used:

1. Delivery and Logistics Optimization

Companies like Sell on Amazon , UPS供应链解决方案 , and FedEx Freight need to plan delivery routes in a way that minimises fuel costs, avoids unnecessary detours, and ensures all packages are delivered in the right order. Just like in Zip, the challenge is to connect multiple destinations efficiently while following certain constraints.

2. Autonomous Robots and Warehouse Management

Many modern warehouses, especially those using automated robots (like Amazon Robotics or Tesla’s Gigafactories), rely on algorithms that help machines move efficiently between shelves. These robots must follow optimized paths to pick up and drop off items quickly, much like how you must connect the numbers in Zip without wasting moves.

3. PCB Design and Circuit Routing

In electronics, designing a printed circuit board (PCB) requires engineers to connect different components while avoiding overlaps and minimising wire length. The same fundamental logic used in Zip applies here—finding the best way to make all necessary connections while working within a confined space.

4. Public Transportation and Ride-Sharing Services

Apps like Uber , Lyft , and TFI Local Link Kerry (bus networks) can use algorithms similar to the Zip puzzle to optimize routes. Ride-sharing services must determine the best way to pick up and drop off passengers in the most efficient order, reducing unnecessary travel time and fuel consumption.

5. Pathfinding in Video Games and AI

Many video games use pathfinding algorithms to help characters move intelligently across maps. The logic behind these movements—whether in open-world games or AI-driven NPCs—relies on the same type of planning you use to solve a Zip puzzle.

Math model

We need to

• Create a closed path visiting all nodes just once
• The visit order should be respected
• The transition can only happen between two neighbour cells.

Here is the Python code developed in ORtools (CP-SAT) Solver

In ZIP puzzle, you see a thick black line which indicates that the move between those cells is not allowed. Simply we can set the lateral between those two nodes = 0 .

Final Thoughts

While Zip may seem like just a fun puzzle, it actually mirrors the complex challenges faced in logistics, robotics, electronics, and AI. By solving these puzzles, you are unknowingly training your brain to think like an optimization engineer—a skill that has practical applications in the real world.

Next time you play, think about how companies and technologies around the world rely on the same logic to deliver packages, guide robots, design circuits, and optimize transportation systems. Pretty cool, right?

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