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Rows and columns

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Text version of this lesson

Totals along both axes pin a board down faster than any single clue.

Key takeaway: Always start from the most constrained row or column: the one with the fewest ways left to be filled.

  1. Question 1

    Which lights are ON?

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    Why: One per row and one per column means the lights form a permutation: each choice removes a column for everyone else.

    Hint: Row A has only one column left open.

  2. Question 2

    Which lights are ON?

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    Why: The chain runs from the most constrained cell outward: find the row with one option left and repeat.

    Hint: Column 1 is barred for rows B and C, and row A is already placed. Only one row can take it.

  3. Question 3

    Which lights are ON?

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    Why: Row totals and column totals must agree — both add up to five, and that cross-check is what makes the grid solvable.

    Hint: Row B needs two lights but cannot use column 1, so it takes both remaining columns.

  4. Question 4

    Which lights are ON?

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    Why: Once column 1 forces a light into both remaining rows, each of them has exactly one slot left to fill.

    Hint: Row B is done after its single light, so columns 1, 2 and 4 must be filled by rows A and C.

  5. Question 5

    Which lights are ON?

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    Why: A column total equal to the number of rows fills the whole column at once — the strongest clue on the board.

    Hint: Column 1 has as many lights as there are rows, so every row is lit there.

  6. Question 6

    Which lights are ON?

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    Why: Parity turned three separate columns into three separate instructions, and the exclusion picked which row went where.

    Hint: Row A holds three of the four columns, and column 4 is not one of them.