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The phrase "put two and two together" is correct and used in written English.
It is used to mean that someone has come to a logical conclusion by connecting the different pieces of evidence. For example: "With all the clues, I was able to put two and two together and figure out the surprise party."
Exact(60)
Everyone has put two and two together".
"People put two and two together sometimes".
I put two and two together, and voilà!
"Put two and two together, and it makes four".
"People might put two and two together".
Let's put two and two together".
"I couldn't put two and two together," she said.
But people are going to put two and two together.
Then Pearl, at last, put two and two together.
I like to put two and two together.
"I'll let you put two and two together".
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com