each of the four adjacent stones <is/are> part of

[Omega Force]

Hello.

Which of these sentences is the correct one? :

- A real eye is an eye in which each of the four adjacent stones are part of a living group
- A real eye is an eye in which each of the four adjacent stones are part of living groups
- A real eye is an eye in which each of the four adjacent stones is part of a living group
- A real eye is an eye in which each of the four adjacent stones is part of living groups

"Real eye", "eye" and "living group" are just terms used in the game of Go. You don't need to know what they mean exactly to be able to answer my question.

But note that "each of the four adjacent stones" can be part of four different living groups, three different living groups, two different living groups or (most commonly by far) one different living group.

Thanks in advance for your answers.

 

[Rhye]

"Each" is singular and thus you would say "Each... is". I believe that both the last two options are possible, but option 4 gives the implication that one stone can/must be a part of multiple groups (which I don't think is the case), therefore option 3 is best.