1. The state or quality of being vague, unclear, or being open to many interpretations: The ambiguousness, or uncertainty, of Jack’s answer didn’t help Elizabeth understand why he was looking for a new job.
2. The vagueness of something which makes people hesitant to accept what has been presented by someone: The ambiguousness of the mayor’s plans for the new city hall created a lot of confusion in the minds of the citizens.

When the speaker used the ambiguousness of "1 + 2 = 3", Mark didn't know if the man meant "one man plus two women", or "one woman plus two men", or "a father, a mother, plus a child", as shown in the illustration below.