# Equation for a falling coin tower

I'm referring to the following experiment- https://www.stevespanglerscience.com/lab/experiments/coin-tower/

For a given mass of identical coins stacked upon the other, and a given impulse with which the knife/striker hits the lower coin, is it possible to determine at what threshold number of coins the tower will fall over? What factors are to be considered like torque, inertial mass, centre of gravity etc. Consider the coefficient of friction between coins as 'x' and the ground to be frictionless.

I considered the lower coin to be one system and the rest of the tower as another system. I have written two equations for the impulse force using the change in momentum for the striker as well as the lower coin. But I'm lost after this as it is an impulsive force hence I cannot find minimum force to ensure the rest of the tower falls, any insight would be helpful. Note how the friction between the coins is maximum between the lowest and the second lowest coin and decreases as one moves up the tower.

What I understand is, with each collision of the striker with the lowest coin, the coins shift from their places to an opposite direction. And this shift increases as one moves up the tower with decrease in friction. So as a whole the centre of gravity of the tower shifts by some distance. Only when the centre of gravity shifts outside the bottom coin the tower will fall. But how do I determine that using the relevant equations?