Stanley's Saga

Discrete Mathematics Level 3

The protagonist of this story, Stanley, is standing peacefully at coordinates \( (0, \space 0) \) without any concern in his life whatsoever.

Now, Stanley will move at coordinates \( (3, \space 4) \).

If Stanley only goes either up, or right, or up-right (corresponding vectors in their respective order: \( \vec{u}(0, \space 1) \), \( \vec{r}(1, \space 0) \) , \( \vec{ur}(1, \space 1) \)), on how many ways can Stanley accomplish this tremendous stunt?

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.