Fish Tank Puzzle Solved: Top View Shortest Path 2026

The fish tank puzzle challenges your spatial reasoning: given a fish swimming in a 2m high, 1m wide, 1m deep tank, you must find the top view of the shortest path that matches given front and side views. This classic geometry problem tests your ability to visualize 3D paths from 2D projections. Here’s how to solve it step by step.

Understanding the Fish Tank Puzzle

The puzzle presents a fish swimming along a path inside a rectangular tank. You are shown the path from the front, the right side, and the top. Your task is to deduce the top view of the shortest possible path that produces the given front and side views.

This requires analyzing the constraints imposed by each projection. The front view tells you the vertical and horizontal positions as seen from the front, while the side view gives you depth information. The top view combines both to reveal the actual 3D route.

Solution Strategy for the Fish Tank Puzzle

To solve the puzzle, you must break down the path into segments and determine which planes each segment must lie on. The key is to use the cross-sections defined by the views.

Step 1: Analyze the Front and Side Views

Start by identifying the vertical and horizontal lines in the front view. These define planes that cut through the tank. For example, a vertical line in the front view corresponds to a vertical plane at a certain depth, while a horizontal line corresponds to a horizontal plane at a certain height.

In the first example, the diagonal segment of the path must lie on the plane defined by the vertical line in the front view. Similarly, the horizontal segment lies on that same plane. The final segment must be on the shaded area indicated in the solution.

Step 2: Determine the Top View

Once you know which planes each segment lies on, you can project these onto the top view. The top view shows the x and z coordinates (width and depth), ignoring height. By mapping each segment to its correct plane, you can draw the shortest possible path in the top view.

For the second example, the bottom half of the path must fall on a shaded cross-section, and the top half on another. The shortest path is found by connecting these sections with straight lines, respecting the constraints.

Comparison of the Two Puzzle Solutions

Key Takeaways for Solving Geometry Puzzles

• Break the path into segments based on the views.
• Identify the planes each segment must lie on.
• Use the shortest distance principle to connect segments.
• Project the 3D path onto the top view for the final answer.

Why This Puzzle Matters

This puzzle is a great exercise in spatial visualization, a skill used in fields like engineering, architecture, and computer graphics. It also demonstrates how 2D representations can encode 3D information, a concept fundamental to technical drawing and CAD.

By practicing such puzzles, you improve your ability to think in three dimensions, which is valuable in many STEM careers.

FAQ

We hope this breakdown helps you understand the fish tank puzzle. If you enjoyed this challenge, look for more puzzles from the 1729 Maths School, which aims to nurture young mathematicians.

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