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Tracing Conducting Paths Across Two Tiles 4 questions

Tracing Conducting Paths Across Two Tiles

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A floor sensor uses square tiles made of conducting squares, marked M, and insulating squares. A current path can cross from one M square to another only when they share a full edge. The current contacts touch every square along the two edges being tested.

Both tiles have rows A–E and columns 1–5. In P all cells in rows B and D conduct; the rest are insulating. In Q all cells in columns 2 and 4 conduct; the rest are insulating.
Tile models. M marks a conducting square.
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Question 1

Which tile can conduct from its left edge to its right edge without changing any squares?

  1. P only
  2. Q only
  3. Both tiles
  4. Neither tile

Question 2

The two tiles each have ten M squares. Name one complete path in each tile and identify the opposite edges it connects.

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The team turns square C2 in Q into an insulating square. No other squares change.

Question 3

Explain whether Q still has a top-to-bottom path. Identify the path or the break that determines your answer.

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Question 4

Return to tile P. Name three squares to change to M for a path from row A to row E. Explain why at least three squares must change.

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