
Nate the Great and the Phony Clue by Marjorie Weinman Sharmat, 1977.
One day, as Nate is coming back from a run with his dog, Sludge, he finds a torn piece of paper on his doorstep that says “VITA.”

Realizing that this odd word is actually part of a longer word in a message, he decides to hunt down the rest of it.
Thinking that perhaps Rosamond’s cats may have found the message and torn it, he goes to Rosamond’s house. When he gets there, he sees that more of the message is up in a tree with Big Hex.
Even when Nate gets that piece, it still doesn’t tell him the full story of the message. It seems that someone is inviting Nate to come to their house at three that afternoon, but without a name or address, how will Nate know where to go?
It looks like there’s still one more piece missing from the message, so he begins looking for it. One of the other boys in the neighborhood, Finley, says that he doesn’t think Nate is really as “Great” as he says he is, and he doubts that Nate will find what he’s looking for. When Finley walks away, dropping a piece of paper behind him, Nate thinks that perhaps Finley is giving him a clue.
It turns out that the paper that Finley dropped says “phony clue” on it. However, Finley’s “phony clue” turns out to be the clue that Nate needs to solve the mystery!

My Reaction and Spoilers
This test of Nate the Great’s detective skills is actually a test set up by Finley and his friend, Pip, who have a bet about whether or not Nate will put all the pieces together by three o’clock. I thought that might be the case from the beginning, but I’m not sure whether that’s because the mystery is obvious or if I helf-remembered the solution to the mystery from when I first read the book when I was a kid.