'''
    When is the probability that in an image
    with N pixels, c point-like objects 
    will not occupy the same pixel < 0.5 ?
    
    Multiply probabilities of consequtive c
    people not overlapping
'''

N = 365
ratio = 1.
c = 0
while(c < N):   # c is the number of people
    c += 1
    ratio = ratio *(N-c+1)/N  # no overlap
    p = 1 - ratio             # overlap
    print("#",c,"P(none), P(some)",ratio,p)
    if (p < 0.5): overlap = c+1
        
print(" # overlapping b-days =", overlap)
    
    
# now you can tidy up the output
# with np.around(x,digits)
# or C/Fortran-style formatting