Either Side vs Both Sides vs Each Side

Irish Stones

Happy New Year to everybody!
I'm here to ask you for help about an issue.
Either side vs Both sides vs Each side
Let's say that I have a tree on one side of the house and another identical tree on the other side of the house.
Should I say:
-There's a tree on either side of the house
-There's a tree on both sides of the house
-There's a tree on each side of the house
I have made some researches on google and it came out that "either side" means "mutually exclusive", that is "There's a tree EITHER on this side of the house OR on the other side of the house, but not on both sides.
But I also found some web pages where who wrote the articles said "either side" to mean "both sides", so now the dilemma is that probably all sentences are correct, or who wrote the articles wasn't very good with their own language.
Could you help me, please?

odds_on

If you substitute John for the tree and river for the house, you might get a different perspective. Which seems possible?

John is on either side of the river.
John is on both sides of the river.
John is on each side of the river.

Either followed by a singular nouns usually means one or the other:
John is leaving on either Monday or Tuesday.

However, in expressions containing "either side" or "either end" it can mean both sides, as in your examples.

Similarly, there is a statue on both sides of the gate.

If we use the plural, "there are statues on both sides of the gate" would mean that there is more than one statues on each side of the gate.

Note that "each" takes the singular, while "both" takes the plural of the noun following.
There are apples on each tree. (however, there may be many trees)
There are apples on both trees. (here, there are only two trees)

Isn't English great fun to work with? !!!!!! And so very difficult for non native speakers to learn.

Irish Stones

So, in the first sentence John is only on one side of the river, one side or the other side. Not on the two sides at the same moment.
In the other two sentences it seems that we have two John
Only the first is possible, of course.

But it seems that you mean that the sentences
-There's a tree on both ends of the bridge
-There's a tree on each end of the bridge
-There's a tree either end of the bridge
are all correct. Am I right?

Yes, English is fun, but sometimes it hides some tricks
Thanks for your time.

odds_on

All correct.
However, I would actually say:
There's a tree at both ends of the bridge. Although I have definitely heard "on both ends" on many occasions.

Perhaps it is something that is different between Irish English and English English.

pickarooney

"There's a tree at both ends", while it would be understood, actually means the same tree is at each end, so avoid that one and use either of the others.

Irish Stones

pickarooney wrote: »

"There's a tree at both ends", while it would be understood, actually means the same tree is at each end, so avoid that one and use either of the others.

Yes, as a matter of fact, if I pay attention to that sentence, it might sound a little confusing.
Thanks a lot!