The Arithmetic Machine

Algebra Level 1

Alice and Bob have an arithmetic machine. The machine takes in a real number, does some processing and outputs a real number. Specifically, the machine works as follows:

Now suppose the following:

Alice entered a number into the machine and got back 100.
Bob also entered a number and got back 100.

Does this mean that both Alice and Bob entered the same number?

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.