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Cascading lights

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Text version of this lesson

One press moves several lights at once. Plan the presses, not the lights.

Key takeaway: Pressing a switch twice cancels itself, so only the set of switches you press matters, never the order.

  1. Question 1

    Pressing a light flips it and the light to its right.

    Turn every light ON.

    Show answer and explanation

    Why: Two presses do it. Fixing the leftmost light first removes all the guesswork.

    Hint: Only light 1 can be changed by a single switch. Start there.

  2. Question 2

    Pressing a light flips it together with the light on each side.

    Turn every light ON.

    Show answer and explanation

    Why: Order never matters here: only the set of switches you pressed decides the result.

    Hint: Pressing the same switch twice undoes it, so each switch is used once or not at all.

  3. Question 3

    Pressing a light flips everything in its row and everything in its column.

    Leave only the light at row A, column 1 ON.

    Show answer and explanation

    Why: Three presses, and the bulb you never pressed is the one that stays lit.

    Hint: Every press flips exactly three of the four bulbs.

  4. Question 4

    Pressing a light flips the other two, but never itself.

    Leave the red and yellow lights ON, and purple OFF.

    Show answer and explanation

    Why: One press. The switch that leaves itself alone is exactly the one you want.

    Hint: You need the two lights you are not pressing to come on.

  5. Question 5

    Pressing a light flips it and its neighbours above, below, left and right.

    Turn every light ON.

    Show answer and explanation

    Why: Pressing the four corners lights the whole board. Symmetry in the goal points at symmetry in the solution.

    Hint: The target is symmetric, so look for a symmetric set of presses.

  6. Question 6

    Pressing a light flips it and its right-hand neighbour. Light 4 is neighboured by light 1.

    Leave lights 1 and 3 ON, and the rest OFF.

    Show answer and explanation

    Why: Two neighbouring presses shift a lit pair around the ring.

    Hint: In a ring there is no end to start from, so try a pair of neighbouring switches.