Which one of the following could be a complete and accurate list of lights that are on together?

allisonfarley December 17, 2020

scenarios

I made two scenarios using the two options for the lights on the North side. 1 & 3 and 2 & 3. I then realized that the rule that says any 3 consecutive lights has to have one off, might be a sign that the scenarios didn't necessarily help. Does that rule leave too many options for 2 scenarios to depict whats on and off even when noting "on/off" for multiple options for each spot? I noticed the game setup has no scenarios...so I fear that this is a big issue I have. I cannot pinpoint when a scenario is necessary and when it is not. I appreciate any guidance ! Ally

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shunhe December 22, 2020

Hi @allisonfarley,

Thanks for the question! So actually, that’s not a bad way of doing it. If we know lights 1 and 3 are on, we can actually narrow it down to two possibilities. 2 and 7 have to be off because light 1 is on, and light 6 also has to be on, since light 7 (a corner light) is off. So we can’t tell between lights 4 and 5, but we know that both of them can’t be on.

Then, let’s say that lights 2 and 3 are on. Then 4 has to be off to avoid three in a row, And then 5 has to be on. So then we don’t know about 6 and 7, but we do know that exactly one of them is on. So really, there’s only a few ways to solve this game, and the way you set it up is fine.

Hope this helps! Feel free to ask any other questions that you might have.

allisonfarley December 25, 2020

That is so relieving !!! I just went back to my diagram for this game and read through my scenarios while reading your explanation and they matched your explanation perfectly. It is so reassuring to see that my instincts are developing.

Thanks so much for your help Shunhe :)