How many banks does it take for a ball to fall.

//imagine a pool table as a series of grids.

def henrySimulator(): stepsize = 0.001; initialLocation = array([0,0]) inPocket = false;

for angle in range(0,90): ammountOfBanks = 0; ballLocation = (0,0); while !inPocket: ballLocation = ballRolls(ballLocation, angle); inPocket = isInPocket(ballLocation); if bankedOffWall(ballLocation): ammountOfBanks += 1 print ammountOfBanks;

def ballRolls(currentLocation, angle): newLocation = array([0,0]); stepSize = 0.001; newLocation[0] = currentLocation[0] + stepSize; newLocation[1] = currentLocation[1] + math.tan(angle)*stepSize; return newLocation;

def isInPocket(location): if (location[0]%1 == 0) || location[1]%1 == 0 : return true; else: return false;

def bankedOffWall(ballLocation): if ballLocation[0]/3 > 1: return true if ballLocation[1]/2 > 1: return true return false

=================== Try 2

for(x,y) from (0,0)->(1,1) for m from 0 -> inf y=mx+b findIntegerIntersection()