# Brute force search for solutions to 711 puzzle
# x+y+z+r = 711,
# x*y*z*(711-x-y-z) = 711*10**6  
# All prices are in cents.
# All combinations such that x <= y <= z  are generated
# but only if  x <= y <= z <= r the equation is checked.

n = 0
for x in range(1,709):
	for y in range(x,710-x):
		for z in range(y,711-x-y):
			r = 711-x-y-z
	  		if (z <= r): 
				n = n+1
	  			if (x*y*z*r==711000000): print 'x,y,z,r',x,y,z,r,' cents' 
print  ' checked',n,'  cases'