According to the text, there are three ways to solve elastic collision problems. The first way is to find the velocities of the two objects, v1 and v2, by using the conservation of momentum formula. The second way is to find the velocity of the center of mass by using the 22/11 formula. The third way is to use the formula for elastic collision, which involves masses, initial velocities, and kinetic energy. In order to solve an elastic collision problem, one must first identify the masses and velocities of the objects involved and their direction of travel before the collision, and then use the conservation of momentum and kinetic energy formulas to find the solution. This method can also be applied to head-on collisions between two particles, where their movements are considered.