Super-Collider

Probability Level 3

At time t=0t = 0 a particle is at point 00 on the real line. At time t=1t=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=2t = 2, each of these particles gets divided into 22 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=8193t = 8193?

Image credit: Wikipedia CERN
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