friends.py

from random import choice as ch
R = range(1,366)

# report doubles, triples for a single run
def analyze(L):
    L.sort()
    rD = dict()
    i = 0
    while i < len(L) - 2:  # up to penultimate item
        v = L[i]
        j = i + 1
        if L[j] != v:
            i += 1
            continue
        while j < len(L) and L[j] == v:
            j += 1
        n = j - i
        if n in rD:
            rD[n] += 1
        else:
            rD[n] = 1
        i = j + 1
    return rD

#----------------------------------
# run the simulation for my case:  45 friends

N = 45
D = dict()
reps = 1000

for i in range(reps):
    L = [ch(R) for i in range(N)]
    rD = analyze(L)
    s = str(rD)
    if not s in D:
        D[s] = 1
    else:
        D[s] += 1

#----------------------------------
# print the results

revD = dict()
for k,v in D.items():
    revD[v] = k
c = len(str(reps))
for k in sorted(revD.keys(), reverse=True):
    print str(k).rjust(c), revD[k]
print reps