People see 3 and 1 and don't pay attention to the fact that persons and substance are different concepts.
1 person + 1 person + 1 person = 3 persons (not 3 Gods)
the 3 persons are 1 substance, 1 God. But godhood and personhood are not the same kind of thing. God's substance is mysterious, and we can't really say that it is the sum of its parts as you try to do in your question. Someone could say 1a+1a+1a=1b a=5 b=15 to answer your math question, but that wouldn't accurately represent the trinity. It only shows that three of one type of thing can be equivalent to one of another type of thing. And if it's possible here, it might also be possible with the trinity even though it is a somewhat different concept. If you have something large and chop it into small parts, the small parts do not retain the characteristic of largeness, so the largeness is the sum of it's small parts, but the persons of the trinity are all fully deity, so it is not the sum of its parts.
You can't picture it as 1 God + 1 God + 1 God either because there are not three separate Gods to be added. it is mysterious because we don't know a lot about it, But there is no concept of mutual exclusivity which would demonstrate a contradiction.
Not that this is related, but just for fun, in boolean algebra, 1+1+1=1
Because the + does not signify addition, but rather a digital OR, and the number system is binary.
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