Question

What are the minimum number of tile pieces (shown on the right) that are required to create a path from tile A to tile B, such that ALL the following conditions are met:

• All tiles are to be used at least once.
• Tiles cannot overlap.
• The path on a tile must be connected to another path of a tile.
• The same type of tile cannot be used one-after-the other in a sequence.
• Rotation of the tiles is not allowed.
• Exclude tile A and tile B from the count.
  

Answer 1

Correct Answer: 12

To determine the minimum number of tile pieces needed to construct a path from tile A to tile B, considering all the given constraints, follow these steps:

• Identify distinct paths on each tile: Analyze the available tiles and the unique paths on each tile. Ensure each tile type is used at least once and remember that rotation is not allowed, so orientation matters.
• Plan the path: Strategically plan the path from tile A to tile B while following these critical rules:
  • Sequence different tile types continuously since the same type cannot be used consecutively.
  • Ensure paths align properly since they have to be connected.
• Count the tiles: Exclude tile A and tile B from the count and ensure all other tiles are used at least once without overlap.
• Verify against range: Compute the total number of tiles and validate that it aligns with the given range 12 to 12.

By carefully analyzing the tiles' connections and ensuring all constraints are met, the calculated minimum number of tiles is 12. This solution adheres to all criteria: no overlap, different tile sequences, connected paths, and compliance with the given range.