There are three singers Prateek, Akanksha and gurbinder. They are doing a concert to celebrate my awesomeness. I have asked them to sing X distinct number of songs. Though each one of them want to sing all X songs, but due to their limits, each one has to sing P, A and G songs. All songs can be sung by either 1, 2 or 3 of them. Each of the X son…

awesomeness.py

f = lambda i,j: int("{0:b}".format(i+1).zfill(3)[j])

def func(x, p, a, g):
	if(p == 0 and a == 0 and g == 0 and x == 0): return 1
	if(p < 0 or a < 0 or g < 0 or p+a+g < x or x==0): return 0
	l = lambda count, pos: count + func(x-1, p-f(pos,0), a - f(pos,1), g - f(pos,2))
	return reduce(l, range(7), 0)

print func(3,1,1,3) #9
print func(50,10,10,10) #0

Ruby version : https://gist.github.com/prat0318/9299888