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) - 1:  # 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
        sz = j - i        # length of repeat
        if sz in rD:
            rD[sz] += 1
        else:
            rD[sz] = 1
        i = j + 1
    return rD

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

N = 45
D = dict()
reps = 10000

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


'''
> python friends.py 
 2727 {2: 2}
 2251 {2: 3}
 1934 {2: 1}
 1138 {2: 4}
  591 {}
  396 {2: 5}
  248 {2: 1, 3: 1}
  220 {2: 2, 3: 1}
  175 {2: 3, 3: 1}
   85 {3: 1}
   83 {2: 6}
   60 {2: 4, 3: 1}
   17 {2: 5, 3: 1}
   13 {2: 7}
    9 {2: 2, 3: 2}
    7 {4: 1}
    6 {3: 2}
    5 {2: 1, 4: 1}
    3 {2: 6, 3: 1}
    2 {2: 3, 4: 1}
    1 {5: 1}
10000
> 
'''