Super-Collider

Discrete Mathematics Level 3

At time \(t = 0\) a particle is at point \(0\) on the real line. At time \(t=1\), the particle divides into two and instantaneously after division, one particle moves one unit to the left and the other moves one unit to the right. At time \(t = 2\), each of these particles gets divided into \(2\) and one of the two new particles move to the right by 1 unit and the other moves to the left by 1 unit. Whenever two particles meet on the real line they annihilate (destroy) each other completely leaving not a single trace behind.

How many particles will be there at time \(t = 8193\)?

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.