THE QUIET WINGAN OBSERVATORY

03 / GENEROUS PERMISSION, STUBBORN LAMPS

Three lamps, one reasonable request

Lamps A, B and C are all off. On each move, choose any two different lamps and flip both: off becomes on; on becomes off. No other operation is allowed. You may make as many moves as you like. Can you finish with exactly one lamp on? Give a sequence that does it, or a reason no sequence can work. I have been quite generous with the number of moves. The lamps have made no promises.

Plain-text puzzle card · A way to read together

Try the switches

Each button flips the two named lamps. The letters and on/off labels carry the state; colour is merely decoration.

A · off
B · off
C · off

0 moves. A off, B off, C off. 0 lamps on.

Show the recent move record

    The latest 12 moves are shown. A text card keeps the full sequence for up to 200 moves; after that it says the history is partial.

    A note to take with you

    A failed sequence is an observation. What would turn it into an argument about every sequence?

    This work stays in this page. It is not sent, saved to an account, or counted as participation. Reloading may clear it. Copy anything you want to keep.

    A little assistance

    Hint 1 — open only if wanted

    Watch how the number of lit lamps changes in one move, rather than following just one lamp.

    Hint 2 — open only if wanted

    List the three kinds of pair you can flip: two dark lamps, two lit lamps, or one of each.

    Reveal the solution and its reasoning

    No finite sequence of legal moves can leave exactly one lamp on.

    A move flips two lamps. If both were off, the lit count rises by two. If both were on, it falls by two. If one was on and the other off, the count does not change.

    Zero is even. Every move preserves an even lit count, so the requested count of one is unreachable. Allowing more moves does not change that rule.

    Testing a few sequences can suggest this answer. The preserved evenness is what proves it for every finite sequence.

    Plain-text solution

    Bring an observation

    A working argument, a useful mistake, or a kinder sentence: all are welcome.

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    THERE IS ROOM AT THE WINDOW

    Moves and invariants

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