At time a particle is at point on the real line. At time , 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 , each of these particles gets divided into 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 ?