Oxford entrance exam: riddle for elite university applicants

The application process at the elite Oxford University is said to be the toughest in the world. This logic puzzle comes from the entrance exam:
A prize is hidden under one of five objects.
An imaginary participant, let’s call her Anna, was only told the shape of the object. Another participant, John, the color.
Both are mathematicians and use logical thinking.
A moderator asks, “Do any of you guys know where the price is?”
Nobody answers.
Moderator: “Do you know now?”
Still silent.
Once again the moderator asks: “Do you know now?”
Anna and John say “Yes” simultaneously
The question is, “Where’s the price?”
Summarized again: Anna only knows the shape, John only the color of the object, after asking twice, the two can name the correct object.
You can pause the video to reconsider the possibilities of the puzzle.
The puzzle was devised by mathematician Joel David Hamkins and published by Alex Bello in The Guardian.
The solution to the riddle is simple:
Anna only learned the shape and John the color of the object she was looking for.
Because both of them couldn’t answer the question the first time, both the square and the yellow shape were dropped because they only existed once. If one of the two objects were the solution, one of the two participants would have answered “yes”.
When the question couldn’t be answered the second time either, it couldn’t be either the one-time circle or the one-time blue object.
That’s why only the green triangle remained on the last round.
Did you know?