Hint: Combinatorics Q5
An obvious invariant: the number of rooms in which all three lights are on, or all three are off.
We want to show that if this invariant is not zero it can be reduced.
If it's not zero, we go to a "same-state" room and flick a switch. This might reduce the invariant. Hurrah we're done.
If it doesn't then what happened? Can we actually have made the situation worse? What's the logical next room to try? What must eventually happen when we keep doing this?
We want to show that if this invariant is not zero it can be reduced.
If it's not zero, we go to a "same-state" room and flick a switch. This might reduce the invariant. Hurrah we're done.
If it doesn't then what happened? Can we actually have made the situation worse? What's the logical next room to try? What must eventually happen when we keep doing this?
posted by Michael Albert at 7:58 am
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