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Patterns of lights

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Text version of this lesson

A single sentence can describe a whole board. Build the board it describes.

Key takeaway: A rule that mentions a cell's position describes every cell at once — apply it cell by cell and the pattern appears.

  1. Question 1

    Light the grid that follows the rule.

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    Why: That is the main diagonal: position matched to position.

    Hint: Go row by row and ask which column number matches the row letter.

  2. Question 2

    Light the grid that follows the rule.

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    Why: Every row holds two lights: shifting moves a pattern but never changes how much of it there is.

    Hint: Shift row A right by one: the light in column 3 wraps around to column 1.

  3. Question 3

    Light the grid that follows the rule.

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    Why: A count says how many, a placement rule says where. You need both to pin one grid.

    Hint: Each row starts at column 1 and fills right.

  4. Question 4

    Which lights are ON?

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    Why: That is the chessboard pattern: four corners plus the centre.

    Hint: Five is the most you can fit on a three-by-three board without touching.

  5. Question 5

    Light the grid that follows the rule.

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    Why: "Both" narrows twice: first the rows, then the columns. Four lights survive.

    Hint: Only rows B and D qualify, because only 2 and 4 are even.

  6. Question 6

    Light the grid that follows the rule.

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    Why: The middle column is its own mirror image, which is why it stays lit in both rows.

    Hint: Mirroring swaps column 1 with column 3 and leaves column 2 where it is.